Question

Coach Evans recorded the height, in inches of each player on his team. The results are shown.

Team heights (inches)
61, 57, 63, 62, 60, 64, 60, 62, 63
Calculate and interpret the IQRs (interquartile ranges) of the heights for the team. put a step by step

Answer 1

3

Explanation:

Given:

Team heights (inches):

61, 57, 63, 62, 60, 64, 60, 62, 63

To find: IQRs (interquartile ranges) of the heights for the team

Solution:

A quartile divides the number of terms in the data into four more or less equal parts that is quarters.

For a set of data, a number for which 25% of the data is less than that number is known as the first quartile
`(Q_1)`

For a set of data, a number for which 75% of the data is less than that number is known as the third quartile
`(Q_3)`

Terms in arranged in ascending order:

`57,60,60,61,62,62,63,63,64`

Number of terms = 9

As number of terms is odd, exclude the middle term that is 62.

`Q_1` is median of terms
`57,60,60,61`

Number of terms (n) = 4

Median =
`(((n)/(2))^(th) +((n)/(2)+1)^(th) )/(2) =(2^(nd)+3^(rd))/(2) =(60+60)/(2)=(120)/(2)=60`

So,
`Q_1=60`

So, 25% of the heights of a team is less than 60 inches

`Q_3` is the median of terms
`62,63,63,64`

Median =
`(((n)/(2))^(th) +((n)/(2)+1)^(th) )/(2) =(2^(nd)+3^(rd))/(2) =(63+63)/(2)=(126)/(2)=63`

So,
`Q_3=63`

So, 75% of the heights of a team is less than 63 inches

Interquartile range =
`Q_3-Q_1=63-60=3`

The interquartile range is a measure of variability on dividing a data set into quartiles.

The interquartile range is the range of the middle 50% of the terms in the data.

So, 3 is the range of the middle 50% of the heights of the students.