Question

Consider a sample with data values of 26, 27, 20, 15, 30, 34, 28, and 20. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary).

Answer 1

Answer:

$r=19$

$IQR=9$

$SD=5.81$

Step-by-step explanation:

Given the following data set:

$26, 27, 20, 15, 30, 34, 28,20$

To find the range of a data set we have to find the largest and the smallest number of the set and then subtract them.

$26, 27, 20, 15, 30, 34, 28,20$

$34-15=19$

$r=19$

To find the interquartile range we have to subtract the third quartile by the first quartile.

$26, 27, 20, 15, 30, 34, 28,20$

$IQR=Q3-Q1$

$Q1=20$

$Q3=29$

$IQR=29-20=9$

$IQR=9$

To find the standard deviation of a data set we have to use the formula to calculate standard deviation with the given values.

$SD=\frac{(26-25)^2+...+(20-25)^2}{8}$

$SD=\frac{270}{8} =\sqrt{33.75} =5.8094750193111$

$5.8094750193111$

$9>5$

$SD=5.81$

Hope this helps.