Question

To study the physical fitness of a sample of 28 people, the data below were collected representing the number of sit-ups that a person could do in one minute.

42, 70, 81, 48, 40, 63, 58, 54, 29, 66, 49, 48, 76, 42, 65, 57, 46, 57, 55, 60, 34, 40, 32, 27, 40, 9, 68, 120

Determine the lower and upper fences. Are there any outliers according to this criterion?

This needs to be completed by hand and show all your work.

Answer 1

first 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.

9   27   29   32   34   40   40   40   42   42   46   48   48   49   54   55   57   57   58   60   63   65   66   68   70   76   81   120   

So, the bottom half is

9   27   29   32   34   40   40   40   42   42   46   48   48   49   

first quartile of these numbers is 40

third quartile:

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.

9   27   29   32   34   40   40   40   42   42   46   48   48   49   54   55   57   57   58   60   63   65   66   68   70   76   81   120   

So, the upper half is

54   55   57   57   58   60   63   65   66   68   70   76   81   120   

The median of these numbers is 64.

third quartile = 64

IQR ;

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

The third quartile is 64.

The first quartile is 40.

The interquartile range = 64 - 40 = 24.

lower fence : Q1 - 1.5 ( IQR )

= 40 - 1.5 ( 24 )

= 4

Upper fence = Q3 + 1.5 ( IQR )

= 64 + 1.5 ( 24 )

= 100

so in the above data 120 is the outlier because it falls above 100.