Question

Use the accompanying data set to complete the following actions.

a. Find the quartiles.

b. Find the interquartile range.

c. Identify any outliers.

61 61 63 64 63 64 58 55 65 65 59 59 60 57 77

Answer 1

a )

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.

55   57   58   59   59   60   61   61   63   63   64   64   65   65   77   

So, the bottom half is

55   57   58   59   59   60   61   

The median of these numbers is 59.

first quartile : 59

Second quartile :

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

55   57   58   59   59   60   61   61   63   63   64   64   65   65   77   

So, the median is 61 .

Second quartile : 61

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.

55   57   58   59   59   60   61   61   63   63   64   64   65   65   77   

So, the upper half is

63   63   64   64   65   65   77   

The median of these numbers is 64.

third quartile : 64

b)

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

The third quartile is 64.

The first quartile is 59.

The interquartile range = 64 - 59 = 5.

c)

Q3 + 1.5 ( IQR ) = 64 + 1.5 ( 5 ) = 71.5

So, 77 is the outlier