Question 1

The most frequently occurring value in a set of data is called the mode.

Accepted Answer

This statement is true. The mode is the value that appears most frequently in a data set.

Question 2

The coefficient of variation is unitless.

Accepted Answer

This is true. The coefficient of variation (CV) is a measure of relative variability that is calculated as the ratio of the standard deviation to the mean. Since the standard deviation and the mean have the same units, those units cancel out when we calculate the CV leaving us with a unitless value.

Question 3

Average deviation is a common measure of the variability of data containing a set of numbers.

Accepted Answer

The average deviation is not a commonly used measure of variability. More common measures include range, variance, and standard deviation.

Question 4

The lowest appropriate level of measurement for the median is ordinal.

Accepted Answer

The median is a central tendency measure that can be calculated for ordinal, interval, and ratio data. However, it can only be interpreted in an ordinal sense when the data are measured at the ordinal level.

Question 5

Skewness and kurtosis of a data set are measures of the shape of the distribution.

Accepted Answer

Skewness is a measure of the degree of asymmetry in the distribution, while kurtosis is a measure of the degree of peakedness or flatness in the distribution. Therefore, both skewness and kurtosis provide information about the shape of the distribution.

Question 6

Statistical measures used to yield information about the center or the middle parts of a group of numbers are called the measures of central tendency.

Accepted Answer

This statement is true. Measures of central tendency include the mean, median, and mode.

Question 7

Kurtosis is a measure of the association between two numerical variables.

Accepted Answer

Kurtosis is a measure of the shape of the distribution of a single variable, not the association between two variables.

Question 8

For grouped data,the midpoint of each class interval is used to represent all the values in a class interval.

Accepted Answer

This is because the midpoint is the most representative value that can be used to summarize a range of values within a class interval.

Question 9

A nonzero value of the skewness indicates asymmetry of the distribution of the data.

Accepted Answer

Skewness measures the degree of asymmetry of a distribution. A nonzero value indicates that the distribution is not symmetrical. Positive skewness indicates that the tail of the distribution is longer on the positive side, while negative skewness indicates that the tail is longer on the negative side.

Question 10

The average of the squared deviations about the arithmetic mean is called the variance.

Accepted Answer

This is the definition of variance in statistics.

Question 11

Computations of the variance and standard deviation using grouped data are potentially only
approximation of the actual variance and standard deviation.

Accepted Answer

When using grouped data, the computation of the variance and standard deviation involves assuming that all values within a class interval are the same, which can result in some inaccuracy in the final result. Therefore, the computations using grouped data are only approximations of the actual variance and standard deviation.

Question 12

For grouped data,the mode is the class midpoint of the modal class where the model class is the class interval with the greatest frequency.

Accepted Answer

This is the correct definition of mode for grouped data.

Question 13

The sum of deviations about the arithmetic mean is always equal to zero.

Accepted Answer

This is true by definition. The arithmetic mean is the center of the distribution and deviations can be positive or negative. The sum of positive and negative deviations cancel each other out, resulting in a sum of zero.

Question 14

If the mean of a distribution is greater than the median,then the distribution is positively skewed.

Accepted Answer

When the mean is greater than the median, it means that there are some high values that are pulling the average (mean) upwards, causing the distribution to have a longer tail on the right side, thus making it positively skewed.

Question 15

The sample standard deviation is calculated by taking the square root of the population standard deviation.

Accepted Answer

The sample standard deviation is calculated by taking the square root of the sample variance, not the population standard deviation. The formula for calculating sample standard deviation is slightly different from the formula for calculating population standard deviation.

Question 16

The median for ungrouped raw data is more complicated to compute then the median for grouped data.

Accepted Answer

The answer of The median for ungrouped raw data is...

Question 17

It is inappropriate to use the mean to analyze data that are not at least interval level in measurement.

Accepted Answer

The mean is only appropriate for analyzing data that are at least interval level in measurement, as it requires equal intervals between each value. Data that are nominal or ordinal level do not have equal intervals and should be analyzed using other measures of central tendency, such as the mode or median.

Question 18

The most appropriate measure of central tendency for nominal-level data is the median.

Accepted Answer

The most appropriate measure of central tendency for nominal-level data is the mode, which represents the most common category or value observed. The median cannot be calculated for nominal data as it involves ordering the values, which is not possible with categorical data.

Question 19

An appropriate measure of central tendency for ordinal data is the mode.

Accepted Answer

The answer of An appropriate measure of central tendency for...

Question 20

The middle value in an ordered array of numbers is called the mode.

Accepted Answer

The middle value in an ordered array of numbers is called the median, not the mode. The mode is the value that appears most frequently in a set of data.

Quiz 3: Descriptive Statistics