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).
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).
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