Question

Musical megabytes How much disk space

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.