Question

Find the median, first quartile, third quartile, and interquartile range of the data. 40,33,37,54,41,34,27,39,35

Answer 1

Median=37

First quartile=33.5

Third quartile=40.5

Inter-quartile range=7

Range=27

Explanation:

The given data set is ;

40,33,37,54,41,34,27,39,35

We arrange the data set in ascending order to obtain;

{27,33,34,35,37,39,40,41,54}

The median is the middle number {37}

First quartile is the median of the lower half of the ascending set.

{27,33,34,35}

`Q_1=(33+34)/(2)=33.5`

The third quartile is the median of the upper half of the ascending set.

{39,40,41,54}

`Q_3=(40+41)/(2)=40.5`

The inter-quartile range is the the third quartile minus the first quartile.

`IQR=Q_3-Q_1=40.5-33.5=7`

The range is the maximum value minus the least value.

Range=54-27=27