# CDC 2r051 Vol. 3 Statistical Methods

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CDC 2R051 Editon 5
Volume 3. Statistical Methods
URE Questions

Questions and Answers
• 1.

### (401) A natural number is stated as a positive number that

• A.

Has any actual value from zero to infinity.

• B.

Has its own unique properties.

• C.

Can be added or subtracted.

• D.

Can be summed.

Correct Answer
A. Has any actual value from zero to infinity.
Explanation
The correct answer is "has any actual value from zero to infinity." This answer accurately defines a natural number as a positive number that includes all values starting from zero and extending to infinity. It implies that natural numbers have no upper limit and can take on any positive value. The other options in the question, such as having unique properties or being able to be added or subtracted, do not fully capture the definition of a natural number.

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• 2.

### (401) What is the value of 5 ÷ 2 × 6?

• A.

0.3.

• B.

8.4.

• C.

15.0.

• D.

30.0.

Correct Answer
C. 15.0.
Explanation
The value of 5 Ã· 2 Ã— 6 can be calculated by following the order of operations, which is parentheses, multiplication and division (from left to right), and finally addition and subtraction (from left to right). In this case, there are no parentheses or addition/subtraction operations. So, we first divide 5 by 2, which equals 2.5. Then, we multiply 2.5 by 6, which equals 15.0. Therefore, the correct answer is 15.0.

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• 3.

### (401) When using natural numbers, a number placed directly behind brackets, with no sign of operation between, indicates that

• A.

You must multiply and divide before adding and subtracting.

• B.

You can perform the calculation with or without the brackets.

• C.

The brackets should be removed before performing the calculation.

• D.

The quantity within the brackets must be multiplied by that number.

Correct Answer
D. The quantity within the brackets must be multiplied by that number.
Explanation
When using natural numbers, a number placed directly behind brackets, with no sign of operation between, indicates that the quantity within the brackets must be multiplied by that number. This is known as the distributive property in mathematics.

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• 4.

### (401) Which phrase is true regarding signed numbers?

• A.

Only whole numbers are used.

• B.

Negative numbers are not used.

• C.

Dividing by zero is permitted.

• D.

Both positive and negative numbers have values.

Correct Answer
D. Both positive and negative numbers have values.
Explanation
Both positive and negative numbers have values because signed numbers include both positive and negative numbers. Positive numbers represent quantities greater than zero, while negative numbers represent quantities less than zero. This allows for a broader range of values and allows for mathematical operations such as addition, subtraction, multiplication, and division to be performed on signed numbers.

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• 5.

### (401) Compute the difference of the signed numbers –17 – (–10).

• A.

+3.0.

• B.

â€“3.0.

• C.

â€“7.0.

• D.

â€“27.0.

Correct Answer
C. â€“7.0.
Explanation
To compute the difference of the signed numbers -17 - (-10), we can rewrite the expression as -17 + 10. Adding a positive number is the same as subtracting its absolute value, so -17 + 10 is equal to -7. Therefore, the correct answer is -7.0.

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• 6.

### (401) How do you write: “The square root of 25 is 5.” as a mathematical expression?

Correct Answer
D.
Explanation
The mathematical expression for the statement "The square root of 25 is 5" is âˆš25 = 5.

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• 7.

### (402) What is 22 percent of 12?

• A.

1.83.

• B.

2.64.

• C.

18.30.

• D.

26.40.

Correct Answer
B. 2.64.
Explanation
To find 22 percent of 12, we can multiply 12 by 0.22. This gives us 2.64, which is the correct answer.

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• 8.

### (403) Which statistical technique is an example of descriptive statistics?

• A.

Probability.

• B.

Extrapolation.

• C.

Trend analysis.

• D.

Measurement scales.

Correct Answer
D. Measurement scales.
Explanation
Measurement scales is an example of descriptive statistics because it involves the categorization and measurement of data in order to describe and summarize it. Descriptive statistics focuses on organizing, summarizing, and presenting data in a meaningful way, and measurement scales play a crucial role in this process by providing a framework for classifying and quantifying variables. Probability, extrapolation, and trend analysis, on the other hand, are examples of inferential statistics which involve making inferences and predictions based on data.

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• 9.

### (404) In the equation Y=X+2, what does the symbol “Y” represent?

• A.

Exponent.

• B.

Inequality.

• C.

Subscript.

• D.

Variable.

Correct Answer
D. Variable.
Explanation
In the equation Y=X+2, the symbol "Y" represents a variable. In algebraic equations, variables are used to represent unknown quantities or values that can vary. In this equation, "Y" is the variable that represents the value that is being calculated or solved for. The equation states that "Y" is equal to the value of "X" plus 2. So, "Y" is the variable that represents the result of adding 2 to the value of "X".

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• 10.

### (404) What is the value of 4^3?

• A.

64.

• B.

24.

• C.

12.

• D.

7.

Correct Answer
A. 64.
Explanation
The value of 4^3 can be calculated by multiplying 4 by itself three times. So, 4^3 is equal to 4 * 4 * 4, which equals 64.

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• 11.

### (405) A sample of a population that is taken in such a manner that each value has an equal chance of being selected is referred to as a?

• A.

Biased sample

• B.

Random sample

• C.

Sampling theory

• D.

Sampling application

Correct Answer
B. Random sample
Explanation
A random sample is a sample of a population that is taken in such a manner that each value has an equal chance of being selected. This means that every member of the population has an equal probability of being included in the sample, which helps to ensure that the sample is representative of the population as a whole. Random sampling is important in statistical analysis as it helps to reduce bias and increase the generalizability of the findings to the larger population.

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• 12.

### (405) If you construct a QLP retrieval to select every 8th record, you are using which sampling technique?

• A.

Selective

• B.

Stratified

• C.

Systematic

• D.

Purposeful

Correct Answer
C. Systematic
Explanation
A systematic sampling technique involves selecting every nth element from a population, in this case every 8th record. This method ensures that the selected sample is representative of the entire population, as it follows a predetermined pattern. The other options, selective, stratified, and purposeful sampling techniques, involve different criteria for selecting the sample and do not follow a systematic pattern. Therefore, the correct answer is systematic.

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• 13.

### (406) Which measurement scale consists of equal intervals between scale values and an arbitrary zero point?

• A.

Ratio

• B.

Nominal

• C.

Ordinal

• D.

Interval

Correct Answer
D. Interval
Explanation
The interval measurement scale consists of equal intervals between scale values and an arbitrary zero point. This means that the differences between the values on the scale are meaningful and can be compared. However, the zero point is arbitrary and does not indicate the absence of the measured attribute. This scale allows for the calculation of differences and the determination of relative magnitude between values.

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• 14.

### (406) You are given two pieces of test equipment that must be loaded on a pallet. One piece weighs 125 pounds and the other piece weighs 3.5 times as much. Using the ratio measurement scale, how much does the second piece of equipment weigh?

• A.

375.0 pounds

• B.

415.5 pounds

• C.

437.5 pounds

• D.

500.0 pounds

Correct Answer
C. 437.5 pounds
Explanation
The second piece of equipment weighs 437.5 pounds. This is because the first piece weighs 125 pounds and the second piece weighs 3.5 times as much, which is calculated by multiplying 125 by 3.5. This equals 437.5 pounds.

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• 15.

### (406) Given measurements of 5.0 hours, 10.0 hours, 15.0 hours, and 20.0 hours, what type of data and measurement scale would you use to classify these data items?

• A.

Discrete; ratio

• B.

Discrete; interval

• C.

Continuous; ratio

• D.

Continuous; interbal

Correct Answer
C. Continuous; ratio
Explanation
The given measurements of 5.0 hours, 10.0 hours, 15.0 hours, and 20.0 hours represent continuous data because they can take on any value within a range. The measurement scale used to classify these data items is ratio because the values have a meaningful zero point and can be compared using ratios.

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• 16.

### (407) The second step in making a frequency distribution is to

• A.

Determine the range of the data

• B.

Determine the class interval size

• C.

Range the data from largest to smallest

• D.

Range the data from smallest to largest

Correct Answer
B. Determine the class interval size
Explanation
The second step in making a frequency distribution is to determine the class interval size. This is because the class interval size determines the width of each interval or group in which the data will be organized. By determining the appropriate class interval size, we can ensure that the data is grouped in a meaningful and organized manner, allowing for easier analysis and interpretation of the frequency distribution.

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• 17.

### (407) With a noncumulative frequency distribution range of 3.6, which class interval will give you 18 classes?

• A.

0.1

• B.

0.2

• C.

0.3

• D.

0.4

Correct Answer
B. 0.2
Explanation
The noncumulative frequency distribution range represents the difference between the highest and lowest values in a data set. In this case, the range is 3.6. To find the class interval that will give you 18 classes, you need to divide the range by the number of classes. So, 3.6 divided by 18 equals 0.2. Therefore, the class interval that will give you 18 classes is 0.2.

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• 18.

### (407) One way of comparing class frequencies to the total frequency is by

• A.

Indirect comparison

• B.

Direct comparison

• C.

Visual inspection

• D.

Percentage

Correct Answer
D. Percentage
Explanation
One way of comparing class frequencies to the total frequency is by using percentages. This involves calculating the proportion of each class frequency relative to the total frequency and expressing it as a percentage. This method allows for a clear comparison between different class frequencies and provides a standardized measure that is easily understandable. By using percentages, it is possible to identify the relative importance or contribution of each class to the total frequency.

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• 19.

### (408) What does each rectangle in a histogram represent?

• A.

Value of the data

• B.

One class of data

• C.

Upper and lower limits

• D.

Number of frequencies

Correct Answer
B. One class of data
Explanation
Each rectangle in a histogram represents one class of data. A histogram is a graphical representation of a frequency distribution, where the data is divided into different classes or intervals. The height of each rectangle represents the frequency or number of observations within that particular class. Therefore, each rectangle represents a specific range or class of data values.

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• 20.

### (408) When constructing a frequency polygon, what are plotted against the corresponding midpoints?

• A.

Series of rectangles

• B.

Individual values of data

• C.

Lower limit and baseline

• D.

Frequencies of the various class intervals

Correct Answer
D. Frequencies of the various class intervals
Explanation
When constructing a frequency polygon, the frequencies of the various class intervals are plotted against the corresponding midpoints. The frequency polygon is a graphical representation of the distribution of data, where the midpoints of the class intervals are plotted on the x-axis and the frequencies are plotted on the y-axis. This allows for visualizing the shape and pattern of the data distribution.

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• 21.

### (409) What measure of central tendency is the most typical value in a distribution?

• A.

Mean

• B.

Mode

• C.

Median

• D.

Weighted mean

Correct Answer
B. Mode
Explanation
The mode is the value that appears most frequently in a distribution, making it the most typical value. Unlike the mean and median, the mode is not affected by extreme values or outliers, which may skew the data. Therefore, the mode provides a good representation of the central tendency of a distribution.

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• 22.

### (409) The mode is the only measure of central tendency that can be used with what measurement scale?

• A.

Ratio

• B.

Interval

• C.

Ordinal

• D.

Nominal

Correct Answer
D. Nominal
Explanation
The mode is the only measure of central tendency that can be used with the nominal measurement scale because it only requires categorizing data into distinct categories without any specific order or numerical value. The mode represents the category that appears most frequently in the data, making it applicable for nominal variables where the data is qualitative and cannot be quantitatively compared or ordered.

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• 23.

### (410) Analysts frequently use the median because it is easy to compute and gives a better picture of data than the mean and mode when data are

• A.

Normal

• B.

Skewed

• C.

Incomplete

• D.

Inconclusive

Correct Answer
B. Skewed
Explanation
The correct answer is "skewed". Analysts frequently use the median because it is easy to compute and gives a better picture of data when the data are skewed. Skewness refers to the asymmetry in the distribution of data. When data are skewed, the mean can be heavily influenced by extreme values, making it less representative of the overall data. The median, on the other hand, is less affected by outliers and provides a more accurate measure of central tendency in skewed data.

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• 24.

### (410) The median cannot be used with data from which measurement scale?

• A.

Nominal

• B.

Interval

• C.

Ordinal

• D.

Ratio

Correct Answer
A. Nominal
Explanation
The median cannot be used with data from the nominal measurement scale because the nominal scale only categorizes data into different groups or categories without any numerical or quantitative value. The median is a measure of central tendency that requires numerical values to determine the middle value. Since the nominal scale does not assign numerical values to the categories, it is not possible to calculate the median.

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• 25.

### (410) What must you do first to determine the median from ungrouped data?

• A.

Arrange the data in classes

• B.

Determine the numerical averages

• C.

Determine the total of the values

• D.

Arrange the data in ascending order

Correct Answer
D. Arrange the data in ascending order
Explanation
To determine the median from ungrouped data, the first step is to arrange the data in ascending order. This is because the median is the middle value when the data is sorted in ascending order. By arranging the data in ascending order, it becomes easier to identify the middle value and calculate the median accurately.

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• 26.

### (411) The harmonic mean is used primarily for averaging

• A.

Data of varying weights

• B.

Skewed distributions

• C.

Approximate values

• D.

Rates

Correct Answer
D. Rates
Explanation
The harmonic mean is commonly used for averaging rates because it gives more weight to smaller values. This is useful when calculating rates because it ensures that outliers or extreme values do not disproportionately influence the average. The harmonic mean is calculated by dividing the number of observations by the sum of their reciprocals, which effectively gives more weight to smaller values. Therefore, it is an appropriate measure to use when averaging rates.

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• 27.

### (411) Compute a weighted mean for a distribution containing two values of 3 each, four values of 2 each, and four values of 5 each.

• A.

1.0

• B.

3.4

• C.

6.6

• D.

11.3

Correct Answer
B. 3.4
Explanation
The weighted mean is calculated by multiplying each value by its corresponding weight, summing these products, and dividing by the total number of values. In this case, the calculation would be: (3*2 + 2*4 + 5*4) / (2+4+4) = 34 / 10 = 3.4.

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• 28.

### (411) The arithmetic mean should be weighted when

• A.

Like values are found in a data series

• B.

All items in a series are equal

• C.

A mean of means is desired

• D.

A series cannot be grouped

Correct Answer
C. A mean of means is desired
Explanation
When a mean of means is desired, the arithmetic mean should be weighted. This means that instead of treating each mean equally, certain means are given more importance or weightage based on their significance or relevance in the overall calculation. Weighted means are used when different subsets of data have varying degrees of importance and need to be considered accordingly in the final calculation.

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• 29.

### (411) Three workers perform a similar task. Worker A takes 30 minutes to complete the task and can finish 2 jobs per hour. Worker B takes 20 minutes to complete the task and can complete 3 jobs per hour. Worker C takes 40 minutes to complete the task, and completes 1.5 jobs per hour.  Which calculation method will you use to find the average time it takes to complete the job?

• A.

Harmonic mean

• B.

Arithmetic mean

• C.

Weighted harmonic mean

• D.

Weighted arithmetic mean

Correct Answer
A. Harmonic mean
Explanation
The harmonic mean is the appropriate calculation method to find the average time it takes to complete the job in this scenario. The harmonic mean is used when dealing with rates or speeds, and it gives more weight to slower speeds. Since each worker completes a different number of jobs per hour and takes a different amount of time to complete the task, the harmonic mean will take into account the varying rates of completion and provide a more accurate average time.

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• 30.

### (411) A unique feature of the harmonic mean is it

• A.

Can only be used for grouped data

• B.

Will always be less than the arithmetic means

• C.

Is only used to average skewed distributions

• D.

Is never weighted when varous quantities of the denominator factors are used

Correct Answer
B. Will always be less than the arithmetic means
Explanation
The harmonic mean is a mathematical average that is used to calculate the overall average of a set of numbers. Unlike the arithmetic mean, the harmonic mean gives more weight to smaller values. This means that the harmonic mean will always be less than the arithmetic mean, as it takes into account the reciprocal of the values being averaged. Therefore, the correct answer is that the harmonic mean will always be less than the arithmetic mean.

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• 31.

### (412) For any distribution, the sum of the deviations is

• A.

One

• B.

Zero

• C.

Less than one

• D.

More than one

Correct Answer
B. Zero
Explanation
The sum of the deviations for any distribution is zero because the deviations are calculated as the difference between each data point and the mean. Some data points will be above the mean and some will be below, resulting in positive and negative deviations. When these deviations are summed up, the positive and negative values cancel each other out, resulting in a sum of zero.

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• 32.

### (412) What is the population standard deviation for the following values: 6, 8, 9, 14, and 22? Formula:

• A.

5.7

• B.

6.4

• C.

11.8

• D.

32.5

Correct Answer
A. 5.7
Explanation
The correct answer is 5.7. The population standard deviation is a measure of the amount of variation or dispersion in a set of values. It is calculated using the formula: square root of the sum of the squared differences between each value and the mean, divided by the total number of values. In this case, the calculation yields a result of 5.7.

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• 33.

### (412) In a sample, you have 10 X-values, and each value is equal to 7. What is the standard deviation of the sample? Formula for standard deviation:

• A.

0

• B.

2.6

• C.

14

• D.

49

Correct Answer
A. 0
Explanation
The standard deviation measures the amount of variation or dispersion in a set of values. In this case, all the X-values in the sample are equal to 7. Since there is no variation or deviation from the mean value of 7, the standard deviation is 0.

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• 34.

### (412) As the number of values in a normal distribution sample decreases, the standard deviation

• A.

Becomes more representative of the population

• B.

Become less representative of the population

• C.

Remains the same

• D.

Increases

Correct Answer
B. Become less representative of the population
Explanation
As the number of values in a normal distribution sample decreases, the standard deviation becomes less representative of the population. This is because with fewer values, there is less data available to accurately estimate the variability in the population. The standard deviation is a measure of how spread out the data is, and with a smaller sample size, there is a higher chance of the sample not being representative of the entire population. Therefore, the standard deviation becomes less reliable as an estimate of the population's variability.

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• 35.

### (413) Given a large number of random samples, the mean of all the sample means related to the population mean is

• A.

The same

• B.

Radically different

• C.

Exactly 3 standard deviations apart

• D.

Mor than 3 standard deviations apart

Correct Answer
A. The same
Explanation
When taking a large number of random samples, the mean of all the sample means will be the same as the population mean. This is because the sample means are unbiased estimators of the population mean, meaning that on average they will be equal to the population mean. Therefore, as the number of samples increases, the sample means will converge to the population mean, resulting in the mean of all the sample means being the same as the population mean.

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• 36.

### (413) In estimating the standard error of the mean, for what sample size do you use n–1 in the formula?

• A.

10 or more

• B.

50 or more

• C.

Less than 25

• D.

Less than 30

Correct Answer
D. Less than 30
Explanation
The correct answer is "Less than 30" because when the sample size is less than 30, it is recommended to use n-1 in the formula for estimating the standard error of the mean. This adjustment is made to account for the fact that the sample size is small and the estimate of the population standard deviation may be less accurate. Using n-1 instead of n in the formula helps to provide a more conservative estimate of the standard error.

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• 37.

### (414) A normal distribution contains what two parameters?

• A.

Mean and mode

• B.

Standard error of the mode

• C.

Mean and the standard deviation

• D.

Standard error and the standard deviation

Correct Answer
C. Mean and the standard deviation
Explanation
A normal distribution is characterized by two parameters: the mean, which represents the average value of the distribution, and the standard deviation, which measures the spread or variability of the data around the mean. The mean determines the central tendency of the distribution, while the standard deviation indicates the dispersion of the data points. Therefore, the correct answer is "Mean and the standard deviation."

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• 38.

### If     , what is the estimate of the standard error of the mean of a sample with a standard deviation of 3 and a sample size of 10?

• A.

.3

• B.

.33

• C.

1.0

• D.

5.0

Correct Answer
C. 1.0
Explanation
The estimate of the standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard deviation is 3 and the sample size is 10. Dividing 3 by the square root of 10 gives an estimate of approximately 1.0.

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• 39.

### (414) In a normal distribution, how many standard deviations on each side of the mean contain over 99 percent of the area under the normal area curve within?

• A.

1

• B.

2

• C.

3

• D.

4

Correct Answer
C. 3
Explanation
In a normal distribution, approximately 99 percent of the area under the curve falls within three standard deviations on each side of the mean. This means that the range from three standard deviations below the mean to three standard deviations above the mean contains the majority of the data.

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• 40.

### (414) When plotted on normal probability graph paper, data from a normal distribution shows up as a

• A.

Circle

• B.

Curved line

• C.

Straight line

• D.

Bell-shaped curve

Correct Answer
C. Straight line
Explanation
When plotted on normal probability graph paper, data from a normal distribution shows up as a straight line. This is because the normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean. The straight line on the graph represents the cumulative probability of the data points falling below a certain value. As the data points are evenly distributed on both sides of the mean, the line appears straight.

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• 41.

### (415) If the mean equals 24 and s equals 6, what are the values of the mean ± 2s?

• A.

24 and 48

• B.

18 and 36

• C.

12 and 36

• D.

12 and 24

Correct Answer
C. 12 and 36
Explanation
The given question asks for the values of the mean Â± 2s. The mean is given as 24 and s is given as 6. To find the values of the mean Â± 2s, we need to add and subtract 2 times the value of s from the mean. So, 24 + 2(6) = 24 + 12 = 36, and 24 - 2(6) = 24 - 12 = 12. Therefore, the values of the mean Â± 2s are 12 and 36.

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• 42.

### (415) How many standard deviations are represented by a value of 22 if the  and s = 5?  Formula:

• A.

-2.8

• B.

-1.6

• C.

1.6

• D.

2.8

Correct Answer
C. 1.6
Explanation
A value of 22 is 1.6 standard deviations above the mean if the standard deviation is 5. This can be calculated by subtracting the mean from the value (22 - 0) and dividing the result by the standard deviation (5). The result is 4.4/5 = 0.88. Since the value is above the mean, the answer is positive, so the number of standard deviations is 0.88 or approximately 1.6.

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• 43.

### (416) Where does the most frequent value of a normal curve occur?

• A.

At the center of the distribution

• B.

At all points in the distributions

• C.

At the tail end of the distribution

• D.

Away from the center of the distribution

Correct Answer
A. At the center of the distribution
Explanation
The most frequent value of a normal curve occurs at the center of the distribution. In a normal distribution, the data is symmetrically distributed around the mean. The peak of the curve, known as the mode, represents the value that occurs most frequently in the data set. Since the normal curve is symmetrical, the mode is located at the center of the distribution where the curve is highest. Therefore, the correct answer is "At the center of the distribution."

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• 44.

### (417) The causes of variation that can be identified on a control chart, regulated, and possibly eliminated are

• A.

Natural

• B.

Random

• C.

Assignable

• D.

Due to chance

Correct Answer
C. Assignable
Explanation
The correct answer is "assignable". Assignable causes of variation are those that can be identified on a control chart, regulated, and possibly eliminated. These causes are not due to chance or random variation, but rather they are specific and identifiable factors that can be controlled or adjusted to improve the process.

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• 45.

### (417) The purpose of a control chart in statistics is to

• A.

Identify causes for variation

• B.

Eliminate causes for variation

• C.

Detect the presence of chance causes for variation

• D.

Detect the presence of assignable causes for variation

Correct Answer
D. Detect the presence of assignable causes for variation
Explanation
A control chart in statistics is a tool used to monitor and track variation in a process over time. It helps to distinguish between natural variation (chance causes) and variation caused by specific factors (assignable causes). By detecting the presence of assignable causes for variation, a control chart allows for the identification and elimination of these causes, leading to improved process performance and quality.

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• 46.

### (418) When identifying processes out of control and using a control chart, what action should you take if you have set your control limits at three standard deviations and later find not enough time is spent looking for assignable causes?

• A.

Switch to tighter limits

• B.

Recalculate the standard deviation

• C.

Keep established limits and do not investigate

• D.

Discard current data and recalculate the standard deviation

Correct Answer
A. Switch to tighter limits
Explanation
If not enough time is spent looking for assignable causes, it means that there is a higher chance of missing any potential issues or problems in the process. To ensure that any out of control processes are identified, it is recommended to switch to tighter control limits. Tighter limits will increase the sensitivity of the control chart and make it easier to detect any variations or assignable causes. This will help in maintaining the quality and stability of the process.

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• 47.

### (419) In statistical terms, what does the control chart for plotting individual X values use for the centerline?

• A.

Mean

• B.

Mode

• C.

Standard deviation

• D.

Standard error of the mean

Correct Answer
A. Mean
Explanation
The control chart for plotting individual X values uses the mean for the centerline. This means that the average value of the X values is used as a reference point on the control chart. By using the mean as the centerline, any deviations from the mean can be easily identified and analyzed for potential causes or issues.

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• 48.

### (419) The statistical interpretation of a control chart for individuals would be distorted if the

• A.

Distribution is normal

• B.

Distribution is extremely skewed

• C.

Standard deviation is too small

• D.

Standard deviation is to large

Correct Answer
B. Distribution is extremely skewed
Explanation
If the distribution of the data in a control chart for individuals is extremely skewed, it means that the data is not evenly distributed and is heavily concentrated towards one side. This can lead to a distortion in the statistical interpretation of the control chart because the assumptions of normality may not hold. Control charts are typically based on the assumption of a normal distribution, so when the distribution is extremely skewed, the control limits and other statistical measures may not accurately represent the process being monitored.

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• 49.

### (420) A statistical chart for averages is used to plot

• A.

Control limits

• B.

Individual values

• C.

Standard deviations

• D.

Means of small samples

Correct Answer
C. Standard deviations
Explanation
A statistical chart for averages is not used to plot control limits or individual values. Control limits are typically plotted on a control chart to determine if a process is in control or out of control. Individual values are plotted on a scatter plot or line graph to show the variation of data points over time or across different variables. A statistical chart for averages, also known as an average chart or X-bar chart, is used to plot the means of small samples taken from a population. This helps to monitor the central tendency of the data and detect any shifts or trends in the process. Therefore, the correct answer is standard deviations.

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• 50.

### (420) What characteristic of the distribution used in a control chart for averages gives it an advantage over a chart for individuals?

• A.

The distribution of means tends to be normal

• B.

The population must always be normal

• C.

The population can never be skewed

• D.

Individual samples are not used

Correct Answer
A. The distribution of means tends to be normal
Explanation
The distribution of means tends to be normal in a control chart for averages. This is advantageous because the normal distribution allows for more accurate predictions and analysis. It also allows for the use of statistical techniques that assume a normal distribution, making it easier to interpret the data and make informed decisions. Additionally, the normal distribution is well understood and has many established properties, making it a reliable choice for control charts.

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