Question 1

The measure of dispersion that is influenced most by extreme values is the _____.

Accepted Answer

The range, which is the difference between the highest and lowest values in a dataset, is influenced most by extreme values because it only considers these two points and ignores the distribution of the rest of the data.

Question 2

The symbol for _____ is $\rho  $.

Accepted Answer

The symbol $\rho$ is used to represent the population correlation coefficient.

Question 3

The sum of deviations of the individual data elements from their mean is _____.

Accepted Answer

By definition, the mean is the point around which the data values cluster. Therefore, the sum of deviations from the mean will always be zero, since the positive and negative deviations will cancel each other out.

Question 4

The value of the sum of the squared deviations from the mean, i.e., $\Sigma ( x - \bar { x } ) ^ { 2 }$ must always be _____.

Accepted Answer

The sum of the squared deviations from the mean, $\Sigma ( x - \bar { x } ) ^ { 2 }$, involves squaring each deviation, which ensures that each term in the sum is non-negative. Therefore, the total sum must be at least zero, as it cannot be negative.

Question 5

If the variance of a data set is correctly computed with the formula using n − 1 in the denominator, which of the following is true?

Accepted Answer

When the formula for variance is calculated using n-1 in the denominator, it is necessary that the data set is a sample, not a population. Therefore, option A is correct, while options B, C, and D are incorrect.

Question 6

The variance of a sample of 81 observations is 64. The standard deviation of the sample is which of the following?

Accepted Answer

The standard deviation is the square root of the variance, so the standard deviation of the sample is sqrt(64) = 8. Therefore, the best choice is C.

Question 7

Which of the following symbols represents the size of a population?

Accepted Answer

N represents the size of a population in statistical notation.

Question 8

Excel's _____ function can be used to compute the population standard deviation.

Accepted Answer

Excel's function for computing the population standard deviation is STDEV.P, which is not listed among the options.

Question 9

Excel's _____ function can be used to compute the population variance.

Accepted Answer

Excel does not have a function specifically named for computing population variance with the options provided. The correct function for population variance in Excel is VAR.P or VARP, not listed among the options.

Question 10

The weight (in pounds) of a sample of 36 individuals was recorded, and the following statistics were calculated. mean = 160
Range = 60
Mode = 165
Variance = 324
Median = 170
The coefficient of variation is _____.

Accepted Answer

The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. 
CV = (standard deviation / mean) x 100%

Since the standard deviation is the square root of the variance, we can find the standard deviation to be:
Standard deviation = sqrt(variance) = sqrt(324) = 18

Now we can plug in the values: 
CV = (18 / 160) x 100% = 0.1125 x 100% = 11.25%

Therefore, the correct answer is B.

Question 11

The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following?

Accepted Answer

The answer of The standard deviation of a sample of...

Question 12

Excel's _____ function can be used to compute the sample standard deviation.

Accepted Answer

The correct function for computing sample standard deviation in Excel is STDEV.S. Option A (STDEV) is for population standard deviation, Option B (VAR.SQRT) does not exist in Excel, and Option C (STDEv) is a typo with incorrect capitalization.

Question 13

The descriptive measure NOT measured in the same units as the original data is the _____.

Accepted Answer

Variance is calculated as the average of the squared differences from the Mean, and thus, it is not in the same units as the original data. It is in squared units.

Question 14

During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5). The variance of the temperatures of the 10 day period _____.

Accepted Answer

The variance is a measure of how spread out the data is from its mean. It is always non-negative because it involves squaring the differences from the mean. Even though temperatures are negative in this case, squaring them will make them positive. Therefore, the variance of the temperatures of the 10 day period must be at least zero.

Question 15

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is _____.

Accepted Answer

The descriptive measure of dispersion that is based on the concept of deviation about the mean is the standard deviation or variance, neither of which are listed as possible choices. The range and interquartile range are based on specific data points and do not take into account the deviation from the mean, so they are not the correct answer.

Question 16

Excel's _____ function can be used to compute the sample variance.

Accepted Answer

The VAR.S function in Excel is specifically designed to compute the sample variance, making it the correct choice for this purpose.

Question 17

The numerical value of the standard deviation can never be _____.

Accepted Answer

The standard deviation is calculated as the square root of the variance, which is always a non-negative value. Therefore, it can never be negative. The other options are incorrect as the standard deviation can be equal to the variance (option A) and can technically be zero (option B) if all the values in the data set are the same.

Question 18

Which of the following is not a measure of dispersion?

Accepted Answer

The option "50^th percentile" is not a measure of dispersion. It is unclear what this measure is and how it is calculated. The other options, range, standard deviation, and interquartile range, all measure how spread out a set of data is.

Question 19

Which of the following is a measure of dispersion?

Accepted Answer

Interquartile range is a measure of dispersion that represents the range of the middle 50% of a dataset. Percentiles and quartiles are also related to dispersion, but they do not provide a range like the interquartile range does.

Question 20

The coefficient of variation is _____.

Accepted Answer

The coefficient of variation is a measure of relative variability that is calculated as the ratio of the standard deviation to the mean, not any of the options provided.

Quiz 3: Descriptive Statistics: Numerical Measures

The measure of dispersion that is influenced most by extreme values is the _____.

The symbol for _____ is $\rho$ .

The sum of deviations of the individual data elements from their mean is _____.

The value of the sum of the squared deviations from the mean, i.e., $\Sigma ( x - \bar { x } ) ^ { 2 }$ must always be _____.

If the variance of a data set is correctly computed with the formula using n − 1 in the denominator, which of the following is true?

The variance of a sample of 81 observations is 64. The standard deviation of the sample is which of the following?

Which of the following symbols represents the size of a population?

Excel's _____ function can be used to compute the population standard deviation.

Excel's _____ function can be used to compute the population variance.

The weight (in pounds) of a sample of 36 individuals was recorded, and the following statistics were calculated. mean = 160 Range = 60 Mode = 165 Variance = 324 Median = 170 The coefficient of variation is _____.

The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following?

Excel's _____ function can be used to compute the sample standard deviation.

The descriptive measure NOT measured in the same units as the original data is the _____.

During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5) . The variance of the temperatures of the 10 day period _____.

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is _____.

Excel's _____ function can be used to compute the sample variance.

The numerical value of the standard deviation can never be _____.

Which of the following is not a measure of dispersion?

Which of the following is a measure of dispersion?

The coefficient of variation is _____.

Quiz 3: Descriptive Statistics: Numerical Measures

The measure of dispersion that is influenced most by extreme values is the _____.

The symbol for _____ is ρ\rho ρ .

The sum of deviations of the individual data elements from their mean is _____.

The value of the sum of the squared deviations from the mean, i.e., Σ(x−xˉ) 2\Sigma ( x - \bar { x } ) ^ { 2 }Σ(x−xˉ) 2 must always be _____.

If the variance of a data set is correctly computed with the formula using n − 1 in the denominator, which of the following is true?

The variance of a sample of 81 observations is 64. The standard deviation of the sample is which of the following?

Which of the following symbols represents the size of a population?

Excel's _____ function can be used to compute the population standard deviation.

Excel's _____ function can be used to compute the population variance.

The weight (in pounds) of a sample of 36 individuals was recorded, and the following statistics were calculated. mean = 160 Range = 60 Mode = 165 Variance = 324 Median = 170 The coefficient of variation is _____.

The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following?

Excel's _____ function can be used to compute the sample standard deviation.

The descriptive measure NOT measured in the same units as the original data is the _____.

During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5) . The variance of the temperatures of the 10 day period _____.

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is _____.

Excel's _____ function can be used to compute the sample variance.

The numerical value of the standard deviation can never be _____.

Which of the following is not a measure of dispersion?

Which of the following is a measure of dispersion?

The coefficient of variation is _____.

The symbol for _____ is $\rho$ .

The value of the sum of the squared deviations from the mean, i.e., $\Sigma ( x - \bar { x } ) ^ { 2 }$ must always be _____.