5. Calculating standard deviation and variance using the definitional formula Aa

Question

5. Calculating standard deviation and variance using the definitional formula Aa Aa Consider a data set containing the following values: 60 93 84 80 95 99 78 90 The mean of the preceding values is 84.875. The deviations from the mean have been calculated as follows: -24.8758.125 -0.875-4.875 10.125 14.125-6.875 5.125 If this is sample data, the sample variance is 154.98 and the sample standard deviation is 12.45 If this is population data, the population variance is 135.61 and the population standard deviation is 11.65 Suppose the smallest value of 60 in the data was misrecorded as 6. If you were to recalculate the variance and standard deviation with the 6 instead of the 60, your new values for the variance and standard deviation would be larger

Explanation / Answer

Given data set is,

60, 93, 84, 80, 95, 99, 78, 90

From this data we get,

Sample mean = 84.875

Sample variance = 154.98

Sample standard deviation = 12.45

Population variance = 135.61

Population standard deviation = 11.65

Suppose the smallest value of 60 in the data is misrecored as 6 then,

Sample mean = 78.125

Sample variance = 903.27

Sample standard deviation = 30.05

Population variance = 790.36

Population standard deviation = 28.11

If we replaced the smallest value of 80 by 8 then sample variance, sample standard deviation, population variance and population standard deviation increases.

Hence, If you were recalculate the variance and standard deviation with the 6 instead of the 60, your new values for the variance and standard deviation would be larger.

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