Question 1

If the entire sample is changed by adding a fixed constant to each observation,then the mean,variance,and median change by the same fixed amount.

Accepted Answer

Adding a fixed constant to each observation in a sample will change the mean and median by that fixed amount, but the variance will remain unchanged because variance measures the spread of the data points around the mean, not their absolute values.

Question 2

The difference between the mean and an observed value is called the deviation from the mean.

Accepted Answer

The deviation from the mean is the difference between any individual value and the mean of the data set.

Question 3

The most commonly used statistics associated with frequencies are measures of location,measures of variability,and measures of occasion.

Accepted Answer

The most commonly used statistics associated with frequencies are measures of central tendency (such as mean, median, and mode) and measures of variability (such as range and standard deviation). Measures of occasion are not commonly used in statistical analysis.

Question 4

When the data points are scattered,variance is small.

Accepted Answer

When the data points are scattered, it means they are spread out from each other, which results in a larger variability or dispersion of the data. Therefore, the variance is typically larger when the data points are scattered.

Question 5

Frequency data may be used to construct a histogram,or a vertical bar chart.

Accepted Answer

Frequency data is often used to create a histogram or a vertical bar chart to display the distribution of the data.

Question 6

The mode represents the highest peak of the distribution.

Accepted Answer

The mode is the value that appears most frequently in a dataset, representing the highest point of the distribution.

Question 7

In a symmetric distribution,the values on either side of the center of the distribution are the same,and the mean,mode,and median are equal.

Accepted Answer

In a symmetric distribution, the values on either side of the center are the same, and the mean, mode, and median are equal.

Question 8

The Range = X_Largest - X_Smallest.

Accepted Answer

The range is calculated by subtracting the smallest value from the largest value, hence the formula X_Largest - X_Smallest is correct.

Question 9

Measures of location or central tendency include the mean,median,and mode.

Accepted Answer

This statement is true. The mean, median, and mode are all measures of central tendency, which are used to describe where the center of a distribution of data lies.

Question 10

If the kurtosis is positive,the distribution is more peaked than a normal distribution.

Accepted Answer

A positive kurtosis indicates that the distribution has more of its variance in the tails and a sharper peak in the center, making it more peaked than a normal distribution.

Question 11

If all the data points are multiplied by a constant,the interquartile range is multiplied by the same constant.

Accepted Answer

Multiplying all the data points by a constant will not change the relative position of the data points, and therefore will not affect the spread of the middle 50% of the data that is measured by the interquartile range.

Question 12

The tendency of the deviations from the mean to be larger in one direction than in the other is called skewness.

Accepted Answer

Skewness refers to the extent to which a distribution deviates from symmetry, and this can result in larger deviations in one direction than in the other.

Question 13

Mean,median,and mode are measures of variability.

Accepted Answer

Mean, median, and mode are measures of central tendency, not variability. Variance and standard deviation are measures of variability.

Question 14

In a frequency distribution,two variables are considered at a time.

Accepted Answer

In a frequency distribution, only one variable is considered, which is typically the variable being measured or observed. The frequencies of the different values or ranges of this variable are then tabulated to create the frequency distribution.

Question 15

The mean is sensitive to extremely small or extremely large values (outliers).

Accepted Answer

The mean is calculated by summing up all the values and dividing by the total number of values. Outliers, i.e., extremely small or extremely large values, can significantly affect the sum and, subsequently, the mean. Therefore, the mean is sensitive to outliers.

Question 16

The valid percentage column in a frequency distribution represents percentages calculated by excluding the cases with missing values.

Accepted Answer

The valid percentage column in a frequency distribution calculates percentages by excluding missing values, thus only considering the valid (non-missing) cases.

Question 17

If a variable is measured on a nominal scale,the median should be used.

Accepted Answer

If a variable is measured on a nominal scale, the median cannot be used as it requires ranking or ordering of the data which is not possible with nominal scales. For non-ordinal data, mode is the appropriate measure of central tendency.

Question 18

When calculating the standard deviation,we divide by n-1 because the sample is drawn from a population and we are trying to determine how much the responses vary from the mean of the entire population.

Accepted Answer

Dividing by n-1 (where n is the sample size) instead of n corrects the bias in the estimation of the population variance and standard deviation from a sample, making it an unbiased estimator. This adjustment is known as Bessel's correction.

Question 19

The variance can never be negative.

Accepted Answer

The variance is always a non-negative value. It represents the average of the squared deviations from the mean, so it cannot be negative.

Question 20

The measures of location are also known as measures of central tendency because they tend to describe the center of the distribution.

Accepted Answer

Measures of location, such as mean, median, and mode, are used to describe the central tendency of a distribution.

Quiz 15: Frequency Distribution,cross-Tabulation,and Hypothesis Testing