Maths · Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
Find the Standard Deviation of the following data:
Find the Standard Deviation of the following data: \( \mathbf{5}, \mathbf{9}, \mathbf{8}, \mathbf{1 2}, \mathbf{6}, \mathbf{1 0}, \mathbf{6}, \mathbf{8} \)
- A. 2.14
- B. 2.16
- C. 2.15
- D. 2.17
Step-by-step solution
First, compute the mean: (5+9+8+12+6+10+6+8)/8 = 64/8 = 8. Then deviations from mean: -3, 1, 0, 4, -2, 2, -2, 0. Squared deviations: 9, 1, 0, 16, 4, 4, 4, 0. Sum of squares = 38. Variance = 38/8 = 4.75. Standard deviation = sqrt(4.75) ≈ 2.179, which truncated to two decimals is 2.17.
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