Question

The five number summary of a dataset is given as1,7,12,15,20a. An observation is considered an outlier if it is belowb. An observation is considered an outlier if it is above

Answer 1

Give a fiven number data set: 1, 7, 12, 15, 20.

Minimum = 1

Maximum = 20

`\begin{gathered} \text{First quartile = (}(5+1)/(4))^(th)\text{ obs.} \\ =1.5^{th\text{ obs.}} \\ =1^(st)obs.+0.5(2^(nd)obs.-1^(st)obs.) \\ =1+0.5(7-1) \\ =4 \end{gathered}`

`\begin{gathered} Median=((5+1)/(2))^(th)\text{ obs.} \\ =3^(rd)\text{ obs.} \\ =12 \end{gathered}`

`\begin{gathered} \text{Third quartile = (}(3(5+1))/(4))^(th)obs.\text{ } \\ =4.5^(th)obs. \\ =4^(th)obs.+0.5(5^(th)obs.-4^(th)obs.) \\ =15+0.5(20-15) \\ =15+0.5(5) \\ =17.5 \end{gathered}`

Find the interquartile range.

`\begin{gathered} \text{Interquartile range = Third quartile-First quartile} \\ =17.5-4 \\ =13.5 \end{gathered}`

Now,

`\begin{gathered} Q_1-1.5\text{ IQR=}4-1.5(13.5) \\ =-16.25 \end{gathered}`
`\begin{gathered} Q_3+1.5IQR=17.5+1.5(13.5) \\ =37.75 \end{gathered}`

a. An observation is considered an outlier if it is below -16.25.

b. An observation is considered an outlier if it is above 37.75