Consider a data set containing the following values: 80, 94, 93, 106, 91, 90, 96, 99 The mean of the preceding values is 93.625. The deviations from the mean have been calculated as follows: –13.625, 0.375, –0.625, 12.375, –2.625, –3.625, 2.375, 5.375 (a) If this is sample data, the sample variance is ___ and the sample standard deviation is ___. (b) If this is population data, the population variance is ___ and the population standard deviation is ___. (c) Suppose the smallest value of 80 in the data was misrecorded as 8. If you were to recalculate the variance and standard deviation with the 8 instead of the 80, your new values for the variance and standard deviation would be ___ and ___.

a)

And if we replace we got:

And the sample deviation is just the square root of the variance:

b)

And if we replace we got:

And the deviation would be:

c) 8, 94, 93, 106, 91, 90, 96, 99

For this case the new mean would be:

The new sample variance would be:

And the new deviation would be:

Step-by-step explanation:

For this case we have the following data given:

80, 94, 93, 106, 91, 90, 96, 99

The mean calculated from the following formula is:

And the deviations from the mean of the data are:

–13.625, 0.375, –0.625, 12.375, –2.625, –3.625, 2.375, 5.375

Part a

The sample variance is given by the following formula:

And if we replace we got:

And the sample deviation is just the square root of the variance:

Part b

Is the data given comes from a population data then the variance is calculaded as:

And if we replace we got:

And the deviation would be:

Part c

For this case we have this new data:

8, 94, 93, 106, 91, 90, 96, 99

For this case the new mean would be:

The new sample variance would be:

And the new deviation would be:

70,000 + 6,000 + 800 + 30

step-by-step explanation: