Question

Musical megabytes How much disk space
does your music use? Here are the file sizes (in
megabytes) for 18 randomly selected files on
Gabriel's mp3 player. Identify any outliers in the
distribution.
2.4 2.7 1.6
13
6.2
1.3
5.6
1.1 2.2
1.9
2.1
4.7
3.0
1.9
2.5
7.5
500

Answer 1

Given:

Consider the file sizes (in  megabytes) for 18 randomly selected files on  Gabriel's mp3 player are shown in the below figure.

To find:

The outliers in the  distribution.

Solution:

We have, the given data set

2.4, 2.7, 1.6 , 1.3 , 6.2, 1.3, 5.6, 1.1, 2.2, 1.9, 2.1, 4.4, 4.7, 3.0, 1.9, 2.5, 7.5, 5.0

Arrange the data in ascending order.

1.1, 1.3, 1.3, 1.6, 1.9, 1.9, 2.1, 2.2, 2.4, 2.5, 2.7, 3.0, 4.4, 4.7, 5.0, 5.6, 6.2, 7.5,

Divide the data in 4 equal parts.

(1.1, 1.3, 1.3, 1.6), 1.9, (1.9, 2.1, 2.2, 2.4),( 2.5, 2.7, 3.0, 4.4), 4.7, (5.0,5.6, 6.2, 7.5)

It is clear that,

$Q_1=1.9$

$Q_3=4.7$

$IQR=Q_3-Q_1$

$IQR=4.7-1.9$

$IQR=2.8$

Now,

$Interval=[Q_1-1.5IQR,Q_3+1.5IQR]$

$Interval=[1.9-1.5(2.8),4.7+1.5(2.8)]$

$Interval=[-2.3,8.9]$

All the data values lies in the interval [-2.3,8.9]. Therefore, the given data set have no outliers.