Question

Please!!!!!!!!

My question is that the ages of a group of state governors at their inaugurations are listed below
50,38,45,47,53,54,57,40,57,64,58,52
Which is the interquartile range of the data set?
Please help
Thanks

Answer 1

The interquartile range of the data set is: 11 years

Explanation:

The ages of a group of state governors at their inaugurations are listed below :

50,38,45,47,53,54,57,40,57,64,58,52

On arranging our data in increasing order i.e. in ascending order we have:

38 40 45 47 50 52 53 54 57 57 58 64

we divide our data into quartiles.

• The median of the data i.e.
  `Q_2` is the middle value of the set.

Here in thus data the middle value will lie between 52 and 53.

Hence, the median is
`(52+53)/(2)=52.5`

`Q_2=52.5`

• the lower data is given as:

38 40 45 47 50 52

Hence
`Q_1` will lie between 45 and 47 which is 46.

Hence,
`Q_1=46`

• the upper data is given as:

53 54 57 57 58 64

Hence,
`Q_3` will lie between 57 and 57 which is 57.

Hence,
`Q_3=57`

Hence, the interquartile range of the data is given as:
`Q_3-Q_1`

`Q_3-Q_1=57-46=11`.

Hence, the interquartile range is 11 years.