Question

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 52 37 44 42 38 41 48 43 39 36 55 42 35 15 52 39 50 29 30

Answer 1

(a)
`Q_1=36.5,M=Q_2=41,Q_3=46`

(b)
`IQR=9.5`

(c) 15

Explanation:

The given data set is

41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30

Arrange the data in ascending order.

15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55

Divide the data in four equal parts.

(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)

Now,

`Q_1=(36+37)/(2)=36.5`

`M=Q_2=(41+41)/(2)=41`

`Q_3=(44+48)/(2)=46`

`IQR=Q_3-Q_1=46-36.5=9.5`

Range for outlier is

`[Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)]`

`=[22.25,60.25]`

Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.