Maths · Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
In an experiment with 15 observations on then following results were available:
In an experiment with 15 observations on \( x, \) then following results were available: \( \sum x^{2}=2830, \sum x=170 \) One observation that was 20 was found to be wrong and was replaced by the correct value \( 30 . \) Then the corrected variance is:
- A. 78
- B. 188.6666
- C. 177.3333
- D. 8.3333
Step-by-step solution
Original sum = 170, sum of squares = 2830. Replace observation 20 with 30: new sum = 170 - 20 + 30 = 180, new sum of squares = 2830 - 400 + 900 = 3330. New mean = 180/15 = 12. Variance = (3330/15) - 12^2 = 222 - 144 = 78.
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