Question

5) In your opinion, are there any outliers? Justify your answer.

Answer 1

Given:

From the data set,

`\begin{gathered} The\text{ first quartile},Q_1=21.5 \\ The\text{ third quartile},Q_3=28 \\ The\text{ interquartile range}=Q_3-Q_1=28-21.5 \\ IQR=6.5 \end{gathered}`

The most effective way to find all of your outliers is by using the interquartile range (IQR). The IQR contains the middle bulk of your data, hence there could be low outliers or high outliers.

To get low outliers, we use the rule below;

`\begin{gathered} Q_1-(1.5IQR) \\ Any\text{ number below this is a low outlier} \\ \\ Thus, \\ 21.5-(1.5*6.5) \\ =11.75 \\ \\ From\text{ the data set, there is no number less than 11.75} \\ Hence,\text{ no low outlier exists} \end{gathered}`

To get high outliers, we use the rule below;

`\begin{gathered} Q_3+(1.5IQR) \\ Any\text{ number above this is a high outlier} \\ \\ Thus, \\ 28+(1.5*6.5) \\ =37.75 \\ \\ From\text{ the data set, there is no number greater than 37.75} \\ Hence,\text{ no high outlier exists} \end{gathered}`