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 64 63 58 59 58 64 63 60 55 64 59 56 57 7961  64  63  58  59  58  64  63  60  55  64  59  56  57  79

a. Find the quartiles.

The first​ quartile, Q1 is ?

The second​ quartile, Q 2 is?

The third​ quartile, Q 3 is?

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   55   56   56   57   57   58   58   58   58   59   59   59   59   60   60   61   61   63   63   63   63   64   64   64   64   64   64   79   79   

So, the bottom half is

55   55   56   56   57   57   58   58   58   58   59   59   59   59   60

The first quartile of the data set is 58.

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   55   56   56   57   57   58   58   58   58   59   59   59   59   60   60   61   61   63   63   63   63   64   64   64   64   64   64   79   79   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = ( 60+60 ) / 2 = 60

The Second quartile ( median ) of the data set is 60.

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   55   56   56   57   57   58   58   58   58   59   59   59   59   60   60   61   61   63   63   63   63   64   64   64   64   64   64   79   79   

So, the upper half is

60   61   61   63   63   63   63   64   64   64   64   64   64   79   79   

The third quartile of the data set is 64.

( b )

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

The third quartile is 64.

The first quartile is 58.

The interquartile range = 64 - 58 = 6.

( C ) Outliers :

lower fence = Q1 - 1.5 ( IQR )

= 58 - 1.5 ( 6 )

= 49

UPPER FENCE = Q3 + 1.5 ( IQR )

= 64 + 1.5 ( 6 )

= 73

Therefore,

79 ,79 are outliers