Question

The test scores for a math class are shown below.

83, 85, 82, 93, 83, 84, 95, 87, 86, 94
What is the standard deviation of the data set? Round your answer to the nearest tenth.
A. 4.8
B. 4.6
C. 4.7
D. 4.3

Answer 1

5.5 is the answer, I just took the test

Answer 2

c. 4.7

Explanation:

first, you find the mean of data set:

83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94 = 872/10 = 87.2

then, you take each number and subtract the mean and square it:

(87.2 - 83)² = (4.2)² = 17.64

(87.2 - 85)² = (2.2)² = 4.84

(87.2 - 82)² = (5.2)² = 27.04

(93 - 87.2)² = (5.8)² = 33.64

(87.2 - 83)² = (4.2)² = 17.64

(87.2 - 84)² = (3.2)² = 10.24

(95 - 87.2)² = (7.8)² = 60.84

(87.2 - 87)² = (0.2)² = 0.04

(87.2 - 86)² = (1.2)² = 1.44

(94 - 87.2)² = (6.8)² = 46.24

now, find the mean of the squared numbers:

17.64 + 4.84 + 27.04 + 33.64 + 17.64 + 10.24 + 60.84 + 0.04 + 1.44 + 46.24 = 219.6/10 = 21.96

then, take the square root of the number you just got:

√21.96 = 4.68

and last but not least, round to the nearest tenth: 4.7