Answer:
The interquartile range of the data set is: 11 years
Step-by-step 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. [tex]Q_2[/tex] is the middle value of the set.
Here in thus data the middle value will lie between 52 and 53.
Hence, the median is [tex]\dfrac{52+53}{2}=52.5[/tex]
[tex]Q_2=52.5[/tex]
- the lower data is given as:
38 40 45 47 50 52
Hence [tex]Q_1[/tex] will lie between 45 and 47 which is 46.
Hence, [tex]Q_1=46[/tex]
- the upper data is given as:
53 54 57 57 58 64
Hence, [tex]Q_3[/tex] will lie between 57 and 57 which is 57.
Hence, [tex]Q_3=57[/tex]
Hence, the interquartile range of the data is given as: [tex]Q_3-Q_1[/tex]
[tex]Q_3-Q_1=57-46=11[/tex].
Hence, the interquartile range is 11 years.
