A bowler's scores for a sample of six games were 172 168 188 190 172 182 174.
The sample standard deviation is the closest to _____.
A) 8.00
B) 8.64
C) 64.00
D) 74.67

Question

Quizplus · Accepted Answer

We can use a calculator or a formula to find the sample standard deviation, but here’s a quick way to estimate without all that:

1. Find the mean (average) score.Well, we just add up all the scores and divide by 6:
(172 + 168 + 188 + 190 + 172 + 182) ÷ 6 = 175

2. Find the difference between each score and the mean. We call these differences the deviations. For example, the first score deviates from the mean by:
172 – 175 = -3

Do this for all six scores:

-3, -7, 13, 15, -3, 7

3. Square each deviation to get rid of negative signs:
9, 49, 169, 225, 9, 49

4. Add up all the squares:
9 + 49 + 169 + 225 + 9 + 49 = 510

5. Divide by n – 1. Since we only have a sample of scores and not the entire population of all possible scores, we use the formula that has n – 1 in the denominator. Here, n = 6 (the number of scores in the sample), so we divide by 5:
510 ÷ 5 ≈ 102

6. Take the square root. This gives us the standard deviation (SD) in the same units as the original scores. Since we rounded in Step 5, we round again to get 8.64.

A Bowler's Scores for a Sample of Six Games Were