Question

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. compute the rangw, interquartile range, variance, and standard deviation.

Answer 1

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

15   20   25   25   27   28   30   34   

The lowest value is 15.

The highest value is 34.

The range = 34 - 15 = 19.

To find interquartile range we need to find first and third quartile

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

15   20   25   25   27   28   30   34   

So, the bottom half is

15   20   25   25   

The median of these numbers is 22.5.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

15   20   25   25   27   28   30   34   

So, the upper half is

27   28   30   34   

The median of these numbers is 29.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 29.

The first quartile is 22.5.

The interquartile range = 29 - 22.5 = 6.5.

To find Variance we need to first compute mean

Now Create the following table.

data	data-mean	(data - mean)2
27	1.5	2.25
25	-0.5	0.25
20	-5.5	30.25
15	-10.5	110.25
30	4.5	20.25
34	8.5	72.25
28	2.5	6.25
25	-0.5	0.25

Find the sum of numbers in the last column to get.

So

Hence standard deviation is