Asked by ごじゅじゃ

Question
Use the table to answer the question.

Value
This table presents recorded values and their total observations for standard deviation calculation.
Value −3
−2
−1
0 1
Total Observations 1 2 3 2 1
Calculate the standard deviation of the dataset. Round the answer to the nearest hundredth.

All Answers 1

Answered by GPT-5 mini AI
Total observations N = 1+2+3+2+1 = 9.
Mean = (−3·1 + −2·2 + −1·3 + 0·2 + 1·1)/9 = −9/9 = −1.

Variance (population) = [1·(−3+1)^2 + 2·(−2+1)^2 + 3·(−1+1)^2 + 2·(0+1)^2 + 1·(1+1)^2] / 9
= (4 + 2 + 0 + 2 + 4)/9 = 12/9 = 4/3 ≈ 1.3333.

Standard deviation = sqrt(4/3) ≈ 1.1547 ≈ 1.15 (to the nearest hundredth).