Question 1

What is the range of the data set: 14, 18, 9, 23, 31, 40, 5?

Accepted Answer

The range of a data set is the difference between the maximum and minimum values in the data set. Here, the maximum value is 40 and the minimum value is 5. Therefore, Range = Maximum value - Minimum value = 40 - 5 = 35.

Question 2

Which of the following is not a measure of dispersion?

Accepted Answer

Measures of dispersion include range, mean deviation, variance, and standard deviation. Arithmetic mean is a measure of central tendency, not dispersion. Therefore, arithmetic mean is the correct choice.

Question 3

The sum of the squares of the deviations of the observations from their mean is always:

Accepted Answer

A fundamental property in statistics is that the sum of the squares of the deviations of a set of observations is minimum when taken from their arithmetic mean, and it is always a minimum compared to any other point, hence it is unique and non-negative, specifically being the least for the mean.

Question 4

What is the mean deviation about the mean for the data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21, 11?

Accepted Answer

First, find the mean of the data. Sum = 126, N = 12, Mean = 126/12 = 10.5. The absolute deviations from 10.5 are calculated and averaged to get the mean deviation, which evaluates to 5.25.

Question 5

If the variance of a data set is 16, what is its standard deviation?

Accepted Answer

The standard deviation is defined as the positive square root of the variance. Therefore, Standard Deviation = sqrt(Variance) = sqrt(16) = 4.

Statistics