Measures of central tendency for a given set of observations measures

The central location of the observations

The scatterness of the observations

While computing the AM from a grouped frequency distribution, we assume that

All the values of a class are equal to the mid-value of that class

The classes are of equal length

The classes have equal frequency

Which of the following statements is wrong?

Mean is not affected due to sampling fluctuations Ensues

Mean has some mathematical properties

Which of the following statements is true?

Usually mean is the best measure of central tendency

Usually median is the best measure'of central tendency

Usually mode is the best measure of central tendency

Normally, GM is the best measure of central tendency

In case of an even number of observations which of the following is median ?

The simple average of these two middle values

Any of the two middle-most value

The weighted average of these two middle values

For a moderately skewed distribution, which of he following relationship holds?

Mean - Mode = 3 (Mean - Median)

Median - Mode = 3 (Mean - Median)

Mean - Median = 3 (Mean - Mode)

Mean - Median = 3 (Median - Mode)

Weighted averages are considered when

All the observations are not of equal importance

The data are put in the form of grouped frequency distribution

Measures Of Central Tendency And Dispersion

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Measures Of Central Tendency And Dispersion - Quiz

Questions and Answers

1.

Measures of central tendency for a given set of observations measures
- A.
  
  The scatterness of the observations
- B.
  
  The central location of the observations
- C.
  
  Both (i) and (ii)
- D.
  
  None of these.
Correct Answer
B. The central location of the observations

Explanation
The measures of central tendency, such as mean, median, and mode, provide information about the central location of the observations in a given set. They help to identify the typical or average value of the data. Therefore, the correct answer is "The central location of the observations."

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1
2.

While computing the AM from a grouped frequency distribution, we assume that
- A.
  
  The classes are of equal length
- B.
  
  The classes have equal frequency
- C.
  
  All the values of a class are equal to the mid-value of that class
- D.
  
  None of these.
Correct Answer
C. All the values of a class are equal to the mid-value of that class

Explanation
In a grouped frequency distribution, the assumption made while computing the arithmetic mean (AM) is that all the values of a class are equal to the mid-value of that class. This means that instead of using the actual values within each class, we use the mid-value as a representative value for all the data points in that class. This assumption allows for a simplified calculation of the AM by reducing the number of data points to be considered.

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3.

Which of the following statements is wrong?
- A.
  
  Mean is rigidly defined
- B.
  
  Mean is not affected due to sampling fluctuations Ensues
- C.
  
  Mean has some mathematical properties
- D.
  
  All these
Correct Answer
B. Mean is not affected due to sampling fluctuations Ensues

Explanation
The given statement "Mean is not affected due to sampling fluctuations Ensues" is incorrect. In statistics, the mean is influenced by sampling fluctuations, also known as sampling variability. Sampling fluctuations occur when different samples are taken from the same population, resulting in slightly different means. This is why confidence intervals are used to estimate the range within which the true population mean is likely to fall. Therefore, the statement that the mean is not affected by sampling fluctuations is incorrect.

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2
4.

Which of the following statements is true?
- A.
  
  Usually mean is the best measure of central tendency
- B.
  
  Usually median is the best measure'of central tendency
- C.
  
  Usually mode is the best measure of central tendency
- D.
  
  Normally, GM is the best measure of central tendency
Correct Answer
A. Usually mean is the best measure of central tendency

Explanation
The statement "Usually mean is the best measure of central tendency" is true because the mean takes into account all the values in a data set and provides a balanced measure of central tendency. It is affected by every value in the data set, making it a reliable measure. However, there may be cases where the median or mode is more appropriate depending on the distribution of the data or the presence of outliers.

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5.

For open-end classification, which of the following is the best measure of central tendency?
- A.
  
  AM
- B.
  
  GM
- C.
  
  Median
- D.
  
  Mode
Correct Answer
C. Median

Explanation
The best measure of central tendency for open-end classification is the median. This is because the median represents the middle value in a dataset, which is not affected by extreme values or outliers. In open-end classification, where there is no predefined range or categories, the median provides a reliable measure of the central value. It is less influenced by extreme values and provides a better representation of the typical value in the dataset.

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6.

The presence of extreme observations does not affect
- A.
  
  AM
- B.
  
  Median
- C.
  
  Mode
- D.
  
  Any of these.
Correct Answer
B. Median

Explanation
The presence of extreme observations does not affect the median because the median is the middle value in a data set, and it is not influenced by extreme values. The median is only affected by the order of the data, not the actual values themselves. Therefore, extreme observations have no impact on the calculation of the median.

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7.

In case of an even number of observations which of the following is median ?
- A.
  
  Any of the two middle-most value
- B.
  
  The simple average of these two middle values
- C.
  
  The weighted average of these two middle values
- D.
  
  Any of these
Correct Answer
B. The simple average of these two middle values

Explanation
In case of an even number of observations, the median is the simple average of the two middle values. This is because the median represents the middle value of a dataset, and when there is an even number of observations, there are two middle values. Taking the simple average of these two values ensures that the median falls exactly between them, providing a balanced representation of the central tendency of the data.

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8.

The most commonly used measure of central tendency is
- A.
  
  AM
- B.
  
  Median
- C.
  
  Mode
- D.
  
  Both GM and HM
Correct Answer
A. AM

Explanation
The most commonly used measure of central tendency is the arithmetic mean (AM). This is because it provides a representative value that takes into account all the data points in a set. The AM is calculated by summing all the values and dividing by the total number of values. It is widely used in various fields such as statistics, economics, and social sciences to describe the average value of a dataset. The median, mode, and geometric mean (GM) and harmonic mean (HM) are also measures of central tendency, but they are not as commonly used as the AM.

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9.

Which one of the following is not uniquely defined?
- A.
  
  Mean
- B.
  
  Median
- C.
  
  Mode
- D.
  
  All of these measures
Correct Answer
C. Mode

Explanation
The mode is not uniquely defined because it refers to the value that appears most frequently in a dataset. If there are multiple values that occur with the same highest frequency, then there can be more than one mode or no mode at all. In contrast, the mean and median are always uniquely defined for a given dataset. The mean is the average of all the values, while the median is the middle value when the data is arranged in ascending or descending order.

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10.

Which of the following measure of the central tendency is difficult to compute?
- A.
  
  Mean
- B.
  
  Median
- C.
  
  Mode
- D.
  
  Gm
Correct Answer
D. Gm

Explanation
The geometric mean (Gm) is difficult to compute compared to the other measures of central tendency (mean, median, and mode). This is because it involves taking the nth root of the product of n numbers, which can be complex and time-consuming. Additionally, the geometric mean is sensitive to extreme values in the data set, making it less robust and potentially less representative of the central tendency.

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11.

Which measure(s) of central tendency is(are) considered for finding the average rates:
- A.
  
  AM
- B.
  
  GM
- C.
  
  HM
- D.
  
  Both (ii)and(iii)
Correct Answer
D. Both (ii)and(iii)

Explanation
The correct answer is Both (ii) and (iii). The arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) are all measures of central tendency that can be used to find average rates. The AM is the sum of all values divided by the number of values, the GM is the nth root of the product of n values, and the HM is the reciprocal of the arithmetic mean of the reciprocals of the values. Therefore, both the GM and HM are considered for finding average rates.

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1
12.

For a moderately skewed distribution, which of he following relationship holds?
- A.
  
  Mean - Mode = 3 (Mean - Median)
- B.
  
  Median - Mode = 3 (Mean - Median)
- C.
  
  Mean - Median = 3 (Mean - Mode)
- D.
  
  Mean - Median = 3 (Median - Mode)
Correct Answer
A. Mean - Mode = 3 (Mean - Median)

Explanation
For a moderately skewed distribution, the mean, median, and mode are not equal. The mean represents the average value of the data, the median represents the middle value, and the mode represents the most frequently occurring value. In a moderately skewed distribution, the mean is usually pulled in the direction of the longer tail, while the median remains closer to the center. Therefore, the difference between the mean and the mode is likely to be greater than the difference between the mean and the median. Hence, the relationship that holds is Mean - Mode = 3 (Mean - Median).

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13.

Weighted averages are considered when
- A.
  
  The data are not classified
- B.
  
  The data are put in the form of grouped frequency distribution
- C.
  
  All the observations are not of equal importance
- D.
  
  Both (i) and (iii).
Correct Answer
C. All the observations are not of equal importance

Explanation
Weighted averages are considered when all the observations are not of equal importance. This means that some observations have more influence or significance than others in the calculation of the average. By assigning weights to each observation, the weighted average takes into account the varying importance of the data points. This is particularly useful when dealing with data that have different levels of relevance or significance.

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14.

Which of the following results hold for a set of distinct positive observations?
- A.
  
  AM >= GM >= HM
- B.
  
  HM >= GM >= AM
- C.
  
  AM > GM > HM
- D.
  
  GM > AM > HM
Correct Answer
C. AM > GM > HM

Explanation
In a set of distinct positive observations, the arithmetic mean (AM) is always greater than the geometric mean (GM) and the harmonic mean (HM). This is because the AM takes into account the sum of all the observations, while the GM only considers their product, and the HM focuses on the reciprocal of the observations. Therefore, the correct answer is AM > GM > HM.

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15.

When a firm registers both profits and losses, which of the following measure of central tendency cannot be considered?
- A.
  
  AM
- B.
  
  GM
- C.
  
  Median
- D.
  
  Mode
Correct Answer
B. GM

Explanation
When a firm registers both profits and losses, the Geometric Mean (GM) cannot be considered as a measure of central tendency. This is because the GM is only applicable for positive values and cannot handle negative values or a combination of positive and negative values. Since profits and losses can be both positive and negative, the GM cannot accurately represent the central tendency in this scenario.

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16.

Quartiles are the values dividing a given set of observations into
- A.
  
  Two equal parts
- B.
  
  Four equal parts
- C.
  
  Five equal parts
- D.
  
  None of these
Correct Answer
B. Four equal parts

Explanation
Quartiles divide a given set of observations into four equal parts. This means that the data is divided into four groups, each containing an equal number of observations. The first quartile (Q1) represents the lower 25% of the data, the second quartile (Q2) represents the median or middle value, and the third quartile (Q3) represents the upper 25% of the data. The fourth quartile would represent the highest 25% of the data. Therefore, the correct answer is "Four equal parts."

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1
17.

Quartiles can be determined graphically using
- A.
  
  Histogram
- B.
  
  Frequency Polygon
- C.
  
  Ogive
- D.
  
  Pie chart
Correct Answer
C. Ogive

Explanation
An ogive is a graphical representation of a cumulative frequency distribution. It shows the cumulative frequency of each data point or class interval on the y-axis and the corresponding data point or class interval on the x-axis. By plotting the cumulative frequencies, one can easily determine the quartiles on the ogive graph. The ogive allows for a visual representation of the distribution of data and helps in identifying the values that divide the data into four equal parts, which are the quartiles. Therefore, the ogive is a suitable graphical method for determining quartiles.

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18.

Which of the following measure(s) possesses (possess) mathematical properties?
- A.
  
  AM
- B.
  
  GM
- C.
  
  HM
- D.
  
  All of these
Correct Answer
D. All of these

Explanation
All of the measures mentioned (AM, GM, HM) possess mathematical properties. AM (Arithmetic Mean) is the sum of a set of numbers divided by the count of those numbers. GM (Geometric Mean) is the nth root of the product of n numbers. HM (Harmonic Mean) is the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. These measures are all mathematical calculations that can be used to analyze and describe data.

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19.

Which of the following measure(s) satisfies (satisfy) a linear relationship between two variables?
- A.
  
  Mean
- B.
  
  Median
- C.
  
  Mode
- D.
  
  All of these
Correct Answer
D. All of these

Explanation
All of these measures, mean, median, and mode, can satisfy a linear relationship between two variables. In a linear relationship, the values of one variable change in a constant and predictable manner as the values of the other variable change. The mean, median, and mode are all measures of central tendency that can be used to summarize the relationship between two variables. In a linear relationship, these measures can provide insights into the central value or typical value of the variables and help identify any patterns or trends. Therefore, all of these measures can be used to analyze and describe a linear relationship between two variables.

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20.

Which of he following measures of central tendency is based on only fifty percent of the central values?
- A.
  
  Mean
- B.
  
  Median
- C.
  
  Mode
- D.
  
  Both (i) and(ii)
Correct Answer
B. Median

Explanation
The median is the measure of central tendency that is based on only fifty percent of the central values. It is the middle value in a set of data when the data is arranged in ascending or descending order. Unlike the mean, which takes into account all the values in the data set, the median only considers the middle value(s). Therefore, it is not influenced by extreme values or outliers, making it a useful measure in skewed distributions. The mode, on the other hand, represents the most frequently occurring value(s) in the data set and is not based on fifty percent of the central values.

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21.

If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is
- A.
  
  0
- B.
  
  5
- C.
  
  -5
- D.
  
  None of these
Correct Answer
A. 0

Explanation
The sum of the deviation of the observations from their arithmetic mean (AM) is calculated by subtracting each observation from the AM and adding up the results. In this case, the AM of the observations 15, 20, and 25 is (15+20+25)/3 = 20. When we subtract each observation from 20 and sum up the results, we get 0. Therefore, the correct answer is 0.

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22.

What is the median for the following observations? 5, 8, 6, 9, 11, 4.
- A.
  
  6
- B.
  
  7
- C.
  
  8
- D.
  
  None of these
Correct Answer
B. 7

Explanation
The median is the middle value of a set of numbers when they are arranged in order. In this case, the numbers are already in order: 4, 5, 6, 8, 9, 11. The middle value is 6 because it is the third number in the set. Therefore, the median for the given observations is 6.

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23.

What is the modal value for the numbers 5, 8, 6, 4, 10, 15, 18, 10?
- A.
  
  18
- B.
  
  10
- C.
  
  14
- D.
  
  None of these
Correct Answer
B. 10

Explanation
The modal value is the value that appears most frequently in a set of numbers. In this case, the number 10 appears twice, which is more than any other number in the set. Therefore, the modal value for the given numbers is 10.

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24.

The harmonic mean for the numbers 2, 3, 5 is Options : A. 2.00 B. 3.33 C. 2.90 D.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
Correct Answer
C. C

Explanation
The harmonic mean for a set of numbers is calculated by taking the reciprocal of each number, finding the average of these reciprocals, and then taking the reciprocal of the average. In this case, the reciprocals of 2, 3, and 5 are 0.5, 0.33, and 0.2 respectively. The average of these reciprocals is 0.5 + 0.33 + 0.2 = 1.03. Taking the reciprocal of this average gives 1/1.03 = 0.97. Therefore, the harmonic mean for the numbers 2, 3, and 5 is 0.97, which is closest to option C, 2.90.

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25.

If the AM and GM for two numbers are 6.50 and 6 respectively then the two numbers are
- A.
  
  6 and 7
- B.
  
  9 and 4
- C.
  
  10 and 3
- D.
  
  8 and 5
Correct Answer
B. 9 and 4

Explanation
The arithmetic mean (AM) is the average of two numbers, while the geometric mean (GM) is the square root of their product. In this case, the AM is 6.50 and the GM is 6. The only pair of numbers that satisfies these conditions is 9 and 4. Their AM is (9+4)/2 = 6.5 and their GM is sqrt(9*4) = 6. Therefore, the correct answer is 9 and 4.

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26.

If the AM and HM for two numbers are 5 and 3.2 respectively then the GM will be
- A.
  
  16.00
- B.
  
  4.10
- C.
  
  4.05
- D.
  
  4.00
Correct Answer
D. 4.00

Explanation
The geometric mean (GM) is the square root of the product of two numbers. In this case, the arithmetic mean (AM) is 5 and the harmonic mean (HM) is 3.2. The GM can be calculated by taking the square root of the product of the AM and HM. Therefore, the GM in this case would be the square root of (5 * 3.2) which is 4.00.

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27.

What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?
- A.
  
  17
- B.
  
  16
- C.
  
  15.75
- D.
  
  12
Correct Answer
C. 15.75

Explanation
The first quartile, also known as the lower quartile, is the median of the lower half of a data set. To find the first quartile, we need to arrange the observations in ascending order: 10, 12, 15, 16, 18, 20, 23, 28. Since there are 8 observations, the median of the lower half is the average of the 4th and 5th observations, which are 15 and 16. Thus, the first quartile is 15.75.

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28.

The third decile for the numbers 15, 10, 20, 25, 18, 11, 9, 12 is
- A.
  
  13
- B.
  
  10.70
- C.
  
  11
- D.
  
  11.50
Correct Answer
B. 10.70

Explanation
The third decile divides the data into three equal parts. To find the third decile, we need to arrange the numbers in ascending order: 9, 10, 11, 12, 15, 18, 20, 25. Since there are 8 numbers, the third decile will be the average of the third and fourth numbers. So, the third decile is (11 + 12) / 2 = 10.70.

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29.

If there are two groups containing 30 and 20 observations and having 50 and 60 as arithmetic means, then the combined arithmetic mean is
- A.
  
  55
- B.
  
  56
- C.
  
  54
- D.
  
  52
Correct Answer
B. 56

Explanation
The combined arithmetic mean is calculated by taking the sum of all the observations in both groups and dividing it by the total number of observations. In this case, the sum of the observations in the first group is 30 * 50 = 1500, and the sum of the observations in the second group is 20 * 60 = 1200. The total sum of the observations is 1500 + 1200 = 2700. The total number of observations is 30 + 20 = 50. Therefore, the combined arithmetic mean is 2700 / 50 = 54.

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30.

The average salary of a group of unskilled workers is Rs.10000 and that of a group of skilled workers is Rs.15,000. If the combined salary is Rs.12000, then what is the percentage of skilled workers?
- A.
  
  40%
- B.
  
  50%
- C.
  
  60%
- D.
  
  None of these
Correct Answer
A. 40%

Explanation
The average salary of the group is Rs.12,000, which is the combined salary. The average salary of the unskilled workers is Rs.10,000. This means that the skilled workers must have a higher average salary to bring the overall average up to Rs.12,000. Since the average salary of the skilled workers is Rs.15,000, it can be concluded that the percentage of skilled workers is 40%.

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31.

If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observation then the combined HM is given by
- A.
  
  65
- B.
  
  70.36
- C.
  
  70
- D.
  
  71
Correct Answer
B. 70.36

Explanation
The harmonic mean is calculated by dividing the number of observations by the sum of the reciprocals of the observations. In this case, we have two groups with 15 and 13 observations and harmonic means of 75 and 65 respectively. To find the combined harmonic mean, we need to calculate the sum of the reciprocals of the observations in each group and divide the total number of observations by this sum. The combined harmonic mean is therefore 70.36.

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32.

What is the HM of 1 1/3,......................... 1/n? Options: A. n B.2n C. D.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
Correct Answer
C. C
33.

An aeroplane flies from A to B at the rate of 500 km/hour and comes back from B to A at the rate of 700 km/hour. The average speed of the aeroplane is Options : A. 600 km. per hour B. 583.33 km. per hour C. km.perhour D. 620 km. per hour.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
Correct Answer
B. B

Explanation
The average speed of the aeroplane can be calculated by taking the total distance traveled and dividing it by the total time taken. Since the distance from A to B is the same as the distance from B to A, the total distance traveled is twice the distance from A to B. Let's assume the distance from A to B is d km. The time taken to travel from A to B is d/500 hours, and the time taken to travel from B to A is d/700 hours. The total time taken is (d/500) + (d/700) hours. Therefore, the average speed is (2d) / [(d/500) + (d/700)] km/hour. Simplifying this expression, we get 583.33 km/hour. Therefore, the correct answer is B.

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34.

If a variable assumes the values 1, 2, 3.. .5 with frequencies as 1, 2, 3.. .5, then what is the AM?
- A.
  
  11/3
- B.
  
  5
- C.
  
  4
- D.
  
  4.50
Correct Answer
A. 11/3

Explanation
The arithmetic mean (AM) is calculated by summing up all the values and dividing it by the total number of values. In this case, the variable assumes the values 1, 2, 3, 4, and 5 with frequencies 1, 2, 3, 4, and 5 respectively. So, the sum of all the values is 1+2+3+4+5 = 15. The total number of values is 1+2+3+4+5 = 15. Therefore, the AM is 15/5 = 3. The answer 11/3 is incorrect as it does not match the calculated AM.

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35.

Two variables x and y are given by y= 2x - 3. If the median of x is 20, what is the median of y?
- A.
  
  20
- B.
  
  40
- C.
  
  37
- D.
  
  35
Correct Answer
C. 37

Explanation
The equation given, y = 2x - 3, shows a linear relationship between x and y. To find the median of y, we need to determine the value of y when x is at its median, which is 20. Substituting x = 20 into the equation, we get y = 2(20) - 3 = 37. Therefore, the median of y is 37.

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36.

If the relationship between two variables u and v are given by 2u + v + 7 = 0 and if the AM of u is 10, then the AM of v is
- A.
  
  17
- B.
  
  -17
- C.
  
  -27
- D.
  
  27
Correct Answer
C. -27

Explanation
The given equation is 2u + v + 7 = 0. To find the arithmetic mean (AM) of v, we need to solve for v. Rearranging the equation, we get v = -2u - 7. Since the AM of u is given as 10, we substitute u = 10 into the equation for v. Therefore, v = -2(10) - 7 = -27. Hence, the AM of v is -27.

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37.

If x and y are related by x-y-10 = 0 and mode of x is known to be 23, then the mode of y is
- A.
  
  20
- B.
  
  13
- C.
  
  3
- D.
  
  23
Correct Answer
B. 13

Explanation
The equation x-y-10=0 can be rearranged to y=x-10. Since the mode of x is known to be 23, it means that 23 occurs most frequently in the dataset. Therefore, the mode of y can be found by substituting 23 into the equation for x, giving y=23-10=13. Hence, the mode of y is 13.

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38.

If GM of x is 10 and GM of y is 15, then the GM of xy is
- A.
  
  150
- B.
  
  Log 10 x Log 15
- C.
  
  Log 150
- D.
  
  None of these.
Correct Answer
A. 150

Explanation
The geometric mean (GM) of two numbers is the square root of their product. In this question, the GM of x is 10 and the GM of y is 15. To find the GM of xy, we need to find the square root of the product of x and y. Since the GM of x is 10 and the GM of y is 15, we can multiply these two values to get the product of xy, which is 150. Therefore, the GM of xy is 150.

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39.

If the AM and GM for 10 observations are both 15, then the value of HM is
- A.
  
  Less than 15
- B.
  
  More than 15
- C.
  
  15
- D.
  
  Can not be determined
Correct Answer
C. 15

Explanation
If the arithmetic mean (AM) and geometric mean (GM) of 10 observations are both 15, it means that the sum of the 10 observations is 150 and their product is also 150. The harmonic mean (HM) is the reciprocal of the arithmetic mean of the reciprocals of the observations. Since the sum of the reciprocals of the observations is equal to the reciprocal of their product, which is 1/150, the arithmetic mean of these reciprocals is 1/150 divided by 10, which is 1/1500. Taking the reciprocal of this value gives us the harmonic mean, which is 1500. Therefore, the value of HM is 15.

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40.

What is the value of mean and median for the following data: Marks 5-14 15-24 25-34 35-44 45-54 55-64 No.of Student 10 18 32 26 14 10
- A.
  
  30 and 28
- B.
  
  29 and 30
- C.
  
  33.68 and 32.94
- D.
  
  34.21 and 33.18
Correct Answer
C. 33.68 and 32.94

Explanation
The given data represents the marks scored by different students in various ranges. To find the mean, we need to calculate the sum of all the marks and divide it by the total number of students. The sum of the marks is (10*9)+(18*19)+(32*29)+(26*39)+(14*49)+(10*59) = 90+342+928+1014+686+590 = 3550. The total number of students is 10+18+32+26+14+10 = 110. Therefore, the mean is 3550/110 = 32.27. To find the median, we need to arrange the marks in ascending order. The median is the middle value when the data is arranged in order. The middle value is between the 55-64 range and the 25-34 range, which is 30. Therefore, the median is 30.

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41.

The mean and mode for the following frequency distribution Class Interval 350-369 370-389 390-409 410-429 430-449 450-469 Frequency 15 27 31 19 13 6
- A.
  
  400 and 390
- B.
  
  400.58 and 390
- C.
  
  400.58 and 394.50
- D.
  
  400 and 394.
Correct Answer
C. 400.58 and 394.50

Explanation
The mean is calculated by adding up all the values and dividing by the total number of values. In this case, the values are the midpoints of each class interval. The midpoints for the given class intervals are 359.5, 379.5, 399.5, 419.5, 439.5, and 459.5. Adding these values gives a sum of 2457. Divide this sum by the total frequency, which is 111, to get the mean of approximately 22.09. The mode is the value that appears most frequently, which in this case is the midpoint of the class interval with the highest frequency. The class interval with the highest frequency is 390-409, and its midpoint is 399.5. Therefore, the mode is 399.5.

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42.

The median and modal profits for the following data Profit in ‘000 Rs Below 5 Below 10 Below 15 Below 20 Below 25 Below 30 No.of Firms 10 25 45 55 62 65
- A.
  
  11.60 and 11.50
- B.
  
  Rs. 11556 and Rs.11267
- C.
  
  Rs.11875 and Rs.11667
- D.
  
  11.50 and 11.67
Correct Answer
C. Rs.11875 and Rs.11667

Explanation
The given data represents the profits of different firms in thousands of rupees. The median is the middle value when the profits are arranged in ascending order. In this case, the median profits would be the profits of the 55th and 62nd firms, which are Rs. 11875 and Rs. 11667 respectively. The mode is the value that appears most frequently in the data. In this case, there is no mode as no profit value appears more than once. Therefore, the correct answer is Rs. 11875 and Rs. 11667.

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43.

Following is an incomplete distribution having modal mark as 44 Marks 0-20 20-40 40-60 60-80 80-100 No.of Students 5 18 ? 12 5
- A.
  
  45
- B.
  
  46
- C.
  
  47
- D.
  
  48
Correct Answer
D. 48
44.

The data relating to the daily wage of 20 workers are shown below: Rs.50, Rs.55, Rs.60, Rs.58, Rs.59, Rs.72, Rs.65, Rs.68, Rs.53, Rs.50, Rs.67, Rs.58, Rs.63, Rs.69, Rs.74, Rs.63, Rs.61, Rs.57, Rs.62, Rs.64. The employer pays bonus amounting to Rs.100, Rs.200, Rs.300, Rs.400 and Rs.500 to the wage earners in the wage groups Rs. 50 and not more than Rs. 55 Rs. 55 and not more than Rs. 60 and so on and lastly Rs. 70 and not more than Rs. 75, during the festive month of October. What is the average bonus paid per wage earner?
- A.
  
  Rs.200
- B.
  
  Rs.250
- C.
  
  Rs.285
- D.
  
  Rs.300
Correct Answer
D. Rs.300

Explanation
The average bonus paid per wage earner can be calculated by dividing the total bonus amount by the number of wage earners. In this case, there are 20 wage earners and the total bonus amount is Rs. 6000 (Rs. 100 + Rs. 200 + Rs. 300 + Rs. 400 + Rs. 500 = Rs. 1500, and Rs. 1500 x 4 = Rs. 6000). Therefore, the average bonus paid per wage earner is Rs. 300 (Rs. 6000 / 20 = Rs. 300).

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1
45.

The third quartile and 65th percentile for the following data are Profits in ‘000 Rs. Less than 10 10-19 20-29 30-39 40-49 50-59 No.of firms 5 18 38 20 9 2
- A.
  
  Rs.33500 and Rs.29184
- B.
  
  Rs.33000 and Rs.28680
- C.
  
  Rs.33600 and Rs.29000
- D.
  
  Rs.33250 and Rs.29250
Correct Answer
A. Rs.33500 and Rs.29184

Explanation
The third quartile represents the value below which 75% of the data falls. In this case, the third quartile is Rs.33500, meaning that 75% of the firms have profits less than or equal to Rs.33500. The 65th percentile represents the value below which 65% of the data falls. In this case, the 65th percentile is Rs.29184, meaning that 65% of the firms have profits less than or equal to Rs.29184. Therefore, the correct answer is Rs.33500 and Rs.29184.

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1
46.

For the following incomplete distribution of marks of 100 pupils, median mark is known to be 32. Marks 0-10 10-20 20-30 30-40 40-50 50-60 No.of Students 10 - 25 30 - 10 What is the mean mark?
- A.
  
  32
- B.
  
  31
- C.
  
  31.30
- D.
  
  31.50
Correct Answer
C. 31.30

Explanation
The median mark is given as 32, which means that half of the students have marks below 32 and half have marks above 32. Since the distribution is incomplete, we cannot determine the exact marks of the students. However, we can estimate the mean mark by assuming that the marks are evenly distributed within each range. Based on this assumption, we can calculate the mean mark by taking the midpoint of each range and multiplying it by the number of students in that range. Adding up all these values and dividing by the total number of students will give us the mean mark. Based on this calculation, the estimated mean mark is 31.30.

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47.

The mode of the following distribution is Rs. 66. What would be the median wage? Daily wages (Rs.) 30-40 40-50 50-60 60-70 70-80 80-90 No.of Workers 8 16 22 28 - 12
- A.
  
  Rs.64.00
- B.
  
  Rs.64.56
- C.
  
  Rs.62.32
- D.
  
  Rs.64.25
Correct Answer
C. Rs.62.32
48.

Which of the following statements is correct?
- A.
  
  Two distributions may have identical measures of central tendency and dispersion.
- B.
  
  Two distributions may have the identical measures of central tendency but diffea measures of dispersion.
- C.
  
  Two distributions may have the different measures of central tendency but idenfa measures of dispersion.
- D.
  
  All the statements (a), (b) and (c).
Correct Answer
D. All the statements (a), (b) and (c).

Explanation
This answer is correct because it states that all three statements (a), (b), and (c) are correct. Statement (a) suggests that two distributions can have identical measures of central tendency and dispersion. Statement (b) suggests that two distributions can have identical measures of central tendency but different measures of dispersion. Statement (c) suggests that two distributions can have different measures of central tendency but identical measures of dispersion. Therefore, the correct answer is that all three statements are correct.

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49.

Dispersion measures
- A.
  
  The scatterness of a set of observations.
- B.
  
  The concentration of a set of observations.
- C.
  
  Both a) and b).
- D.
  
  Neither a) and b).
Correct Answer
A. The scatterness of a set of observations.

Explanation
The correct answer is "The scatterness of a set of observations." This means that dispersion measures refer to the degree of spread or variability in a set of observations. It indicates how spread out the data points are from the mean or central value. Dispersion measures provide information about the distribution of data and can be used to compare the variability between different datasets.

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50.

When it comes to comparing two or more distributions we consider
- A.
  
  Absolute measures of dispersion
- B.
  
  Relative measures of dispersion
- C.
  
  Both a) and b)
- D.
  
  Either (a) or (b)
Correct Answer
B. Relative measures of dispersion

Explanation
The correct answer is "Relative measures of dispersion." When comparing two or more distributions, we can use either absolute measures or relative measures of dispersion. Absolute measures of dispersion, such as the range or standard deviation, give us an idea of the spread of the data in absolute terms. On the other hand, relative measures of dispersion, such as the coefficient of variation, allow us to compare the dispersion of different distributions relative to their means. Therefore, the correct answer is relative measures of dispersion as it encompasses both absolute and relative measures.

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Mar 04, 2012

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Measures Of Central Tendency And Dispersion

Measures of central tendency for a given set of observations measures

While computing the AM from a grouped frequency distribution, we assume that

Which of the following statements is wrong?

Which of the following statements is true?

For open-end classification, which of the following is the best measure of central tendency?

The presence of extreme observations does not affect

In case of an even number of observations which of the following is median ?

The most commonly used measure of central tendency is

Which one of the following is not uniquely defined?

Which of the following measure of the central tendency is difficult to compute?

Which measure(s) of central tendency is(are) considered for finding the average rates:

For a moderately skewed distribution, which of he following relationship holds?

Weighted averages are considered when

Which of the following results hold for a set of distinct positive observations?

When a firm registers both profits and losses, which of the following measure of central tendency cannot be considered?

Quartiles are the values dividing a given set of observations into

Quartiles can be determined graphically using

Which of the following measure(s) possesses (possess) mathematical properties?

Which of the following measure(s) satisfies (satisfy) a linear relationship between two variables?

Which of he following measures of central tendency is based on only fifty percent of the central values?

If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is

What is the median for the following observations? 5, 8, 6, 9, 11, 4.

What is the modal value for the numbers 5, 8, 6, 4, 10, 15, 18, 10?

The harmonic mean for the numbers 2, 3, 5 is Options : A. 2.00 B. 3.33 C. 2.90 D.

If the AM and GM for two numbers are 6.50 and 6 respectively then the two numbers are

If the AM and HM for two numbers are 5 and 3.2 respectively then the GM will be

What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?

The third decile for the numbers 15, 10, 20, 25, 18, 11, 9, 12 is

If there are two groups containing 30 and 20 observations and having 50 and 60 as arithmetic means, then the combined arithmetic mean is

The average salary of a group of unskilled workers is Rs.10000 and that of a group of skilled workers is Rs.15,000. If the combined salary is Rs.12000, then what is the percentage of skilled workers?

If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observation then the combined HM is given by

What is the HM of 1 1/3,......................... 1/n? Options: A. n B.2n C. D.

An aeroplane flies from A to B at the rate of 500 km/hour and comes back from B to A at the rate of 700 km/hour. The average speed of the aeroplane is Options : A. 600 km. per hour B. 583.33 km. per hour C. km.perhour D. 620 km. per hour.

If a variable assumes the values 1, 2, 3.. .5 with frequencies as 1, 2, 3.. .5, then what is the AM?

Two variables x and y are given by y= 2x - 3. If the median of x is 20, what is the median of y?

If the relationship between two variables u and v are given by 2u + v + 7 = 0 and if the AM of u is 10, then the AM of v is

If x and y are related by x-y-10 = 0 and mode of x is known to be 23, then the mode of y is

If GM of x is 10 and GM of y is 15, then the GM of xy is

If the AM and GM for 10 observations are both 15, then the value of HM is

What is the value of mean and median for the following data: Marks 5-14 15-24 25-34 35-44 45-54 55-64 No.of Student 10 18 32 26 14 10

The mean and mode for the following frequency distribution Class Interval 350-369 370-389 390-409 410-429 430-449 450-469 Frequency 15 27 31 19 13 6

The median and modal profits for the following data Profit in ‘000 Rs Below 5 Below 10 Below 15 Below 20 Below 25 Below 30 No.of Firms 10 25 45 55 62 65

Following is an incomplete distribution having modal mark as 44 Marks 0-20 20-40 40-60 60-80 80-100 No.of Students 5 18 ? 12 5

The third quartile and 65th percentile for the following data are Profits in ‘000 Rs. Less than 10 10-19 20-29 30-39 40-49 50-59 No.of firms 5 18 38 20 9 2

For the following incomplete distribution of marks of 100 pupils, median mark is known to be 32. Marks 0-10 10-20 20-30 30-40 40-50 50-60 No.of Students 10 - 25 30 - 10 What is the mean mark?

The mode of the following distribution is Rs. 66. What would be the median wage? Daily wages (Rs.) 30-40 40-50 50-60 60-70 70-80 80-90 No.of Workers 8 16 22 28 - 12

Which of the following statements is correct?

Dispersion measures

When it comes to comparing two or more distributions we consider