Question

A Programme Manager has been presented with data related to unauthorisedabsences of the people whom she line manages. The data is shown in Table 3.287AbsencesFrequency9541647 12 4Table 3: Unauthorised absences23a) Explain what an outlier is.b) Calculate the range.c) Calculate the interquartile range.

Answer 1

1) Definition of an Outlier

An outlier is a value in a data set that is very different from the other values. That is, outliers are values unusually far from the middle.

2) Range

The range is the difference between the largest and the smallest number.

Therefore,

The largest absences = 8

The smallest absences = 1

Hence, the range is

`\begin{gathered} 8-1=7 \\ \therefore Range=7 \end{gathered}`

3) Interquartile range

This is calculated by subtracting the value of the first quartile from the value of the third quartile.

The formula for the first quartile is,

`(1)/(4)(N+1)`

with that we get the position of our first quartile.

Firstly, we need to arrange the data given in ascending order.

Given data

`N=\text{Total frequency=12+9+7+4+4+3+2=41}`

Therefore, the first quartile is

`\begin{gathered} (1)/(4)(41+1)=(1)/(4)*42=10.5 \\ \\ \end{gathered}`

Hence, the first quartile is 1.

Let us solve for the third quartile

The formula for the third quartile is,

`(3)/(4)(N+1)`

Hence, the third quartile is

`(3)/(4)(41+1)=(3)/(4)*42=31.5`

Therefore, the third quartile is 5.

Hence, the interquartile range is

`\begin{gathered} 5-1=4 \\ \therefore The\text{ interquartile range=4} \end{gathered}`