Measures Of Central Tendency And Dispersion

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  • 1/100 Questions

    Quartiles are the values dividing a given set of observations into

    • Two equal parts
    • Four equal parts
    • Five equal parts
    • None of these
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About This Quiz

Explore key statistical concepts with our quiz on Measures of Central Tendency and Dispersion. Assess your understanding of mean, median, and how data distributions are measured and interpreted. This quiz is essential for learners aiming to grasp fundamental statistical measures.

Measures Of Central Tendency And Dispersion - Quiz

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  • 2. 

    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

    • 65

    • 70.36

    • 70

    • 71

    Correct Answer
    A. 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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  • 3. 

    The range of 15, 12, 10, 9, 17, 20 is 

    • 5

    • 12

    • 13

    • 11

    Correct Answer
    A. 11
    Explanation
    The range of a set of numbers is calculated by subtracting the smallest number from the largest number. In this case, the smallest number is 9 and the largest number is 20. Therefore, the range is 20 - 9 = 11.

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  • 4. 

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

    • Any of the two middle-most value

    • The simple average of these two middle values

    • The weighted average of these two middle values

    • Any of these

    Correct Answer
    A. 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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  • 5. 

    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

    • 20

    • 13

    • 3

    • 23

    Correct Answer
    A. 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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  • 6. 

    Measures of central tendency for a given set of observations measures  

    • The scatterness of the observations

    • The central location of the observations

    • Both (i) and (ii)

    • None of these.

    Correct Answer
    A. 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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  • 7. 

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

    • 6

    • 7

    • 8

    • None of these

    Correct Answer
    A. 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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  • 8. 

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

    • 18

    • 10

    • 14

    • None of these

    Correct Answer
    A. 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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  • 9. 

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

    • Mean

    • Median

    • Mode

    • Both (i) and(ii)

    Correct Answer
    A. 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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  • 10. 

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

    • 150

    • Log 10 x Log 15

    • Log 150

    • 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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  • 11. 

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

    • Less than 15

    • More than 15

    • 15

    • Can not be determined

    Correct Answer
    A. 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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  • 12. 

    Which measure of dispersion is the quickest to compute? 

    • Standard deviation

    • Quartile deviation

    • Mean deviation

    • Range

    Correct Answer
    A. Range
    Explanation
    The range is the simplest measure of dispersion to compute because it only requires finding the difference between the maximum and minimum values in a dataset. It does not involve any complex calculations or require the use of all the data points. Therefore, it can be quickly calculated even with large datasets, making it the quickest measure of dispersion to compute.

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  • 13. 

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

    • AM

    • GM

    • HM

    • All of these

    Correct Answer
    A. 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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  • 14. 

    For any two numbers SD is always

    • Twice the range

    • Half of the range

    • Square of the range

    • None of these

    Correct Answer
    A. Half of the range
    Explanation
    The correct answer is "Half of the range." This means that for any two numbers, the standard deviation (SD) will always be equal to half of the range between those numbers. The range is the difference between the maximum and minimum values in a set of numbers. Therefore, the standard deviation will be half of this difference.

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  • 15. 

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

    • Mean

    • Median

    • Mode

    • Gm

    Correct Answer
    A. 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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  • 16. 

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

    • 20

    • 40

    • 37

    • 35

    Correct Answer
    A. 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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  • 17. 

    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

    • 17

    • -17

    • -27

    • 27

    Correct Answer
    A. -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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  • 18. 

    If the profitsof a company remains the same for the last ten months,then the standard deviation of profits for these ten months would be ?

    • Positive

    • Negative

    • Zero

    • (a) or (c)

    Correct Answer
    A. Zero
    Explanation
    If the profits of a company remain the same for the last ten months, it means that there is no variation or change in the profits. In other words, all the profit values are identical. When calculating the standard deviation, it measures the dispersion or variability of a set of values from the mean. However, if all the values are the same, the deviation from the mean is zero for each value, resulting in a standard deviation of zero. Therefore, the correct answer is zero.

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  • 19. 

    The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would be

    • 4.90

    • 5.00

    • 4.88

    • 4.85

    Correct Answer
    A. 5.00
    Explanation
    When calculating the standard deviation, each observation is subtracted from the mean, squared, and then the squared differences are averaged. Since one observation was mistakenly recorded as 50 instead of 40, this will affect the calculation of the standard deviation. The correct value for this observation is 40, so the squared difference between the correct value and the mean will be smaller than if it were 50. As a result, the overall sum of squared differences will be smaller, leading to a slightly smaller standard deviation. Therefore, the current value of the standard deviation would be slightly smaller than 5.1, but not as small as 4.85 or 4.88. The answer of 5.00 is the most accurate approximation.

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  • 20. 

    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

    • B

    • C

    • D

    Correct Answer
    A. 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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  • 21. 

    Dispersion measures

    • The scatterness of a set of observations.

    • The concentration of a set of observations.

    • Both a) and b).

    • 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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  • 22. 

    If all the observations are multiplied by 2, then   

    • New SD would be also multiplied by 2

    • New SD would be half of the previous SD

    • New SD would be increased by 2

    • New SD would be decreased by 2.

    Correct Answer
    A. New SD would be also multiplied by 2
    Explanation
    When all the observations are multiplied by 2, it means that each observation is being scaled up by a factor of 2. This will result in the standard deviation (SD) also being scaled up by the same factor of 2. This is because the SD is a measure of the spread or variability of the data, and multiplying all the observations by 2 will increase this spread or variability by the same factor. Therefore, the new SD would be also multiplied by 2.

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  • 23. 

    The appropriate measure of dispersions for open-end classification is 

    • Standard deviation

    • Mean deviation

    • Quartile deviation

    • All these measures

    Correct Answer
    A. Quartile deviation
    Explanation
    The appropriate measure of dispersion for open-end classification is quartile deviation. This measure is suitable because it takes into account the range of values within the data set and provides a measure of the spread of the data. Standard deviation may not be appropriate for open-end classification as it assumes a normal distribution and can be heavily influenced by outliers. Mean deviation is also not suitable as it does not consider the actual values of the data set, but only the deviations from the mean. Therefore, quartile deviation is the most appropriate measure in this case.

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  • 24. 

    The most commonly used measure of central tendency is 

    • AM

    • Median

    • Mode

    • 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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  • 25. 

    Which one of the following is not uniquely defined?

    • Mean

    • Median

    • Mode

    • All of these measures

    Correct Answer
    A. 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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  • 26. 

    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)

    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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  • 27. 

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

    • 11/3

    • 5

    • 4

    • 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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  • 28. 

    Which measure of dispersion is based on all the observations? 

    • Mean deviation

    • Standard deviation

    • Quartile deviation

    • (a) and (b) but not (c)

    Correct Answer
    A. (a) and (b) but not (c)
    Explanation
    The measure of dispersion that is based on all the observations is the standard deviation. Mean deviation and quartile deviation only consider a subset of the observations. Therefore, the correct answer is (a) and (b) but not (c).

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  • 29. 

    The coefficient of mean deviation about mean for the first 9 natural numbers is

    • 200/9

    • 80

    • 400/9

    • 50

    Correct Answer
    A. 400/9
    Explanation
    The coefficient of mean deviation about mean measures the average deviation of each data point from the mean, relative to the mean itself. To calculate it, we first need to find the mean of the first 9 natural numbers, which is (1+2+3+4+5+6+7+8+9)/9 = 5. The mean deviation of each data point from the mean is then calculated as (1-5), (2-5), (3-5), ..., (9-5), which gives us -4, -3, -2, -1, 0, 1, 2, 3, 4. Taking the absolute values of these deviations, we get 4, 3, 2, 1, 0, 1, 2, 3, 4. The sum of these absolute deviations is 20. Dividing this by the number of data points (9) and the mean (5) gives us 20/(9*5) = 400/9, which is the coefficient of mean deviation about mean.

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  • 30. 

    Which of the following statements is wrong?

    • Mean is rigidly defined

    • Mean is not affected due to sampling fluctuations Ensues

    • Mean has some mathematical properties

    • All these

    Correct Answer
    A. 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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  • 31. 

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

    • 6 and 7

    • 9 and 4

    • 10 and 3

    • 8 and 5

    Correct Answer
    A. 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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  • 32. 

    Which measure of dispersion has some desirable mathematical properties?

    • Standard deviation

    • Mean deviation

    • Quartile deviation

    • All these measures

    Correct Answer
    A. Standard deviation
    Explanation
    Standard deviation is the measure of dispersion that has some desirable mathematical properties. It is widely used in statistics and has several advantages, such as being based on all the data points, taking into account the distance of each data point from the mean, and being sensitive to outliers. It is also used in various statistical calculations and hypothesis testing, making it a valuable tool in data analysis.

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  • 33. 

    The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is 

    • 10

    • 20

    • 25

    • 8.30

    Correct Answer
    A. 10
    Explanation
    The quartile deviation is a measure of the spread or dispersion of a dataset. It is calculated as the difference between the upper and lower quartiles. In this case, the upper quartile is 65 and the lower quartile is 45. Therefore, the quartile deviation is 65 - 45 = 20.

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  • 34. 

    Quartiles can be determined graphically using

    • Histogram

    • Frequency Polygon

    • Ogive

    • Pie chart

    Correct Answer
    A. 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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  • 35. 

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

    • Mean

    • Median

    • Mode

    • All of these

    Correct Answer
    A. 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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  • 36. 

    Which measures of dispersions is not affected by the presence of extreme observations?

    • Range

    • Mean deviation

    • Standard deviation

    • Quartile deviation

    Correct Answer
    A. Quartile deviation
    Explanation
    Quartile deviation is not affected by the presence of extreme observations because it is based on the interquartile range, which only considers the middle 50% of the data. This means that extreme values have less influence on the quartile deviation compared to other measures of dispersion such as range, mean deviation, and standard deviation, which take into account all the data points.

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  • 37. 

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

    • AM

    • GM

    • HM

    • Both (ii)and(iii)

    Correct Answer
    A. 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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  • 38. 

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

    • 0

    • 5

    • -5

    • 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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  • 39. 

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

    • 13

    • 10.70

    • 11

    • 11.50

    Correct Answer
    A. 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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  • 40. 

    Which of the following statements is correct?

    • Two distributions may have identical measures of central tendency and dispersion.

    • Two distributions may have the identical measures of central tendency but diffea measures of dispersion.

    • Two distributions may have the different measures of central tendency but idenfa measures of dispersion.

    • All the statements (a), (b) and (c).

    Correct Answer
    A. 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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  • 41. 

    If all the observations are increased by 10, then

    • SD would be increased by 10

    • Mean deviation would be increased by 10

    • Quartile deviation would be increased by 10

    • All these three remain unchanged.

    Correct Answer
    A. All these three remain unchanged.
    Explanation
    If all the observations are increased by 10, the SD (standard deviation), mean deviation, and quartile deviation will all remain unchanged. This is because adding a constant value to each observation does not affect the spread or dispersion of the data. The SD measures the average distance between each data point and the mean, and adding 10 to each observation increases both the mean and the individual distances by the same amount, resulting in no change in the SD. Similarly, the mean deviation and quartile deviation are also measures of dispersion that are not affected by adding a constant value to all observations.

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  • 42. 
    If the mean and SD of x are a and b respectively, then the SD of   is - ProProfs

    If the mean and SD of x are a and b respectively, then the SD of   is

    • -1

    • 1

    • Ab

    • A/b

    Correct Answer
    A. 1
    Explanation
    The standard deviation (SD) is a measure of the dispersion or spread of a dataset. In this question, it is given that the mean and SD of the variable x are a and b respectively. The SD of a constant value is always 0, so it cannot be the answer. The product of the mean and SD (ab) is not a valid measure of SD as it does not reflect the spread of the data. The correct answer is 1, which means that the SD of the variable is equal to b. This implies that the data points are spread out around the mean by a distance of b.

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  • 43. 

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

    • AM

    • GM

    • Median

    • Mode

    Correct Answer
    A. 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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  • 44. 

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

    • 55

    • 56

    • 54

    • 52

    Correct Answer
    A. 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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  • 45. 

    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  

    • 30 and 28

    • 29 and 30

    • 33.68 and 32.94

    • 34.21 and 33.18

    Correct Answer
    A. 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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  • 46. 

    If the relation between x and y is 5y-3x = 10 and the mean deviation about mean for x is 12, then the mean deviation of y about mean is

    • 7.20

    • 6.80

    • 20

    • 18.80

    Correct Answer
    A. 7.20
  • 47. 

    If the SD of x is 3, what is the variance of (5-2x)? 

    • 36

    • 6

    • 1

    • 9

    Correct Answer
    A. 36
    Explanation
    The variance of a constant multiplied by a random variable is equal to the square of the constant multiplied by the variance of the random variable. In this case, the constant is -2 and the random variable is x. Since the variance of x is 3, the variance of (5-2x) is equal to (-2)^2 * 3 = 4 * 3 = 12. However, the answer options provided do not include 12. Therefore, the correct variance of (5-2x) cannot be determined based on the given information.

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  • 48. 

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

    • A

    • B

    • C

    • D

    Correct Answer
    A. 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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  • 49. 

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

    • 17

    • 16

    • 15.75

    • 12

    Correct Answer
    A. 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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  • Aug 16, 2024
    Quiz Edited by
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  • Mar 04, 2012
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    Sweetsalman123
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