Question

l, this page may not function correctly. Click here to learn more. S. Calculating standard deviation and variance using the definitional formula Aa Aa Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The deviations from the mean have been calculated as follows: -0.75 -5.75 0.25 7.25 18.25 2.75-20.75 4.25 and the sample standard deviation is If this is sample data, the sample variance is and the population standard deviation is If this is population data, the population variance is Suppose the largest value of 89 in the data was misrecorded as 80. If you were to recalculate the variance and standard deviation with the 80 instead of the 89, your new values for the variance and standard deviation would be

Answer 1

Solution:

Sample variance = ((-0.75)^2+(-5.75)^2+(0.25)^2+(7.25)^2+(18.25)^2+(-2.75)^2+(-20.75)^2+(4.25)^2)/(8-1) = 875.5/7 = 125.07

Sample standard deviation = sqrt(125.07)= 11.18

Population variance = 875.5/8 = 109.4375

Population standard deviation = 10.46

If value is 80 instead of 89

Than mean = (70+65+71+78+80+68+50+75)/8 = 557/8= 69.625

Sample variance = ((70-69.625)^2+(65-69.625)^2+(71-69.625)^2+(78-69.625)^2+(80-69.625)^2+(68-69.625)^2+(50-69.625)^2+(75-69.625)^2)/(8-1) = 617.875/7= 88.27

Sample standard deviation = sqrt(88.27)= 9.395

Population variance = (617.875/8) = 77.23

Population standard deviation = sqrt(77.23)= 8.79