Given the sample data. x : 22 16 14 31 28 (a) Find the range. (b) Verify that Σ x = 111 and Σ x 2 = 2,681. (c) Use the results of part (b) and appropriate computation formulas to compute the sample...

(a) Find the range.


(b) Verify that Σx = 111 and Σx
² = 2,681.


(c) Use the results of part (b) and appropriate computation formulas to compute the sample variances
² and sample standard deviations.


(d) Use the defining formulas to compute the sample variances
² and sample standard deviations.


(e) Suppose the given data comprise the entire population of allx values. Compute the population variance σ² and population standard deviation σ.

Step 1

(a) Find the range.

Recall that the range is the difference between the largest and smallest values of a data set. In other words, we can subtract the smallest value in the data set from the largest value to find the range. That is,




Recall the given data set.

First, order the data from smallest to largest.

The smallest value is  and the largest value is  . Use these values to calculate the range.