Question

A bowler's scores for six games were 182, 168, 184, 190, 170, and 174. Using these data as a sample, compute the following descriptive statistics:

a. Variance and standard deviation;

Answer 1

The variance is 75.2 and the standard deviation is approximately 8.67.

Step-by-step explanation:

Calculating Variance and Standard Deviation

The question involves calculating the variance and standard deviation for a bowler's scores over six games. First, let us understand what these terms mean. Variance measures how much a set of numbers (scores in this case) are spread out from their average, or mean. The standard deviation is the square root of the variance and provides a measure of the average distance from the mean.

Calculating the Mean:

First, we need to calculate the mean of the scores. The mean is the sum of all the scores divided by the number of scores.

Mean = (182 + 168 + 184 + 190 + 170 + 174) / 6 = 1068 / 6 = 178

Calculating the Variance:

To calculate the variance, sum the squares of the differences between each score and the mean, then divide by the number of scores minus 1.

Variance = [(182 - 178)^2 + (168 - 178)^2 + (184 - 178)^2 + (190 - 178)^2 + (170 - 178)^2 + (174 - 178)^2] / (6 - 1) = (16 + 100 + 36 + 144 + 64 + 16) / 5 = 376 / 5 = 75.2

Calculating the Standard Deviation:

The standard deviation is the square root of the variance.

Standard Deviation = √75.2 ≈ 8.67

Therefore, the variance of the bowler's scores is 75.2, and the standard deviation is approximately 8.67.