Answer to Question #267763 in Statistics and Probability for kath

Question

Find the range, standard deviation, and variance for the given samples. Show your complete

solutions.

1) 1, 2, 5, 7, 8, 19, 22

Answer 1

The greatest number of the set is 22 and the least number is 1. The range of numbers of set is

22 – 1 = 21

The mean of the number is

$\bar{x} = \frac{1+ 2+5+ 7+8+19+ 22}{7} = 9.14$

For each number, calculate the deviation between the number and the mean

Calculate the square of each of the deviations in step 2, and find the sum of these squared deviations.

Because there is a sample of n=7 values, divide the sum 402.63 by (n-1) , which is 6.

Thus the variance is

$s^2 = \frac{402.63}{6} = 67.10$

The standard deviation is

$s = \sqrt{67.10} = 8.2$