Question:
What is the standard deviation of the given data set:
25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
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Standard deviation measures how spread out numbers are from the mean. Use variance = average of squared differences, then take square root.
Updated On: Apr 24, 2025
- 13.33
- 13.31
- 13.14
- 13.08
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The Correct Option is D
Solution and Explanation
First, compute the mean:
Mean = $\dfrac{25 + 50 + 45 + 30 + 70 + 42 + 36 + 48 + 34 + 60}{10} = \dfrac{440}{10} = 44$
Now compute the squared deviations:
$\sum (x_i - \bar{x})^2 = (25-44)^2 + (50-44)^2 + \ldots + (60-44)^2 = 1710$
Variance = $\dfrac{1710}{10} = 171$
Standard Deviation = $\sqrt{171} \approx 13.08$
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