Standard deviation and variance using the definitional formula set containing th

Question

Standard deviation and variance using the definitional formula set containing the following values: 88 96 72 84 95 100 92 90 the preceding values is 89.625. The deviations from the mean have been calculated as follows: -1.625 6.375 -17.625 -5.625 5.375 10.375 2.375 0.375 data, the sample variance is ___ and the sample standard deviation is ____ data, the population variance is ____and the population standard deviation is ___ largest value of 100 in the data was misrecorded as 1, 000. If you were to recalculate the variance and with the 1, 000 instead of the 100, your new values for the variance and standard deviation would _____

Explanation / Answer

Let us calculate the sum of squares of deviations first.

SS = (-1.625)2 + (6.375)2 + (-17.625)2 + (-5.625)2 + (5.375)2 + (10.375)2 + (2.375)2 + (0.375)2

= 2.640625 + 40.640625 + 310.640625 + 31.640625 + 28.890625 + 107.640625 + 5.640625 + 0.140625

= 527.875

Sample variance s2 = SS / (N-1)

= 527.875 / (8 - 1)

= 527.875 / 7

= 75.41

Sample standard deviation s = 75.41 = 8.6839

Population variance 2 = SS / N

= 527.875 / 8

= 65.98

Population standard deviation = 65.98 = 8.12

If the value 100 would be replaced by 1000, the mean deviation and thus the sum of squares would increase. The new values for variance and standard deviation would increase.

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