Answer:
3
Step-by-step 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)](https://tex.z-dn.net/?f=%28Q_1%29)
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)](https://tex.z-dn.net/?f=%28Q_3%29)
Terms in arranged in ascending order:
![57,60,60,61,62,62,63,63,64](https://tex.z-dn.net/?f=57%2C60%2C60%2C61%2C62%2C62%2C63%2C63%2C64)
Number of terms = 9
As number of terms is odd, exclude the middle term that is 62.
is median of terms ![57,60,60,61](https://tex.z-dn.net/?f=57%2C60%2C60%2C61)
Number of terms (n) = 4
Median = ![\frac{(\frac{n}{2})^{th} +(\frac{n}{2}+1)^{th} }{2} =\frac{2^{nd}+3^{rd}}{2} =\frac{60+60}{2}=\frac{120}{2}=60](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Cfrac%7Bn%7D%7B2%7D%29%5E%7Bth%7D%20%2B%28%5Cfrac%7Bn%7D%7B2%7D%2B1%29%5E%7Bth%7D%20%20%7D%7B2%7D%20%3D%5Cfrac%7B2%5E%7Bnd%7D%2B3%5E%7Brd%7D%7D%7B2%7D%20%3D%5Cfrac%7B60%2B60%7D%7B2%7D%3D%5Cfrac%7B120%7D%7B2%7D%3D60)
So, ![Q_1=60](https://tex.z-dn.net/?f=Q_1%3D60)
So, 25% of the heights of a team is less than 60 inches
is the median of terms ![62,63,63,64](https://tex.z-dn.net/?f=62%2C63%2C63%2C64)
Median = ![\frac{(\frac{n}{2})^{th} +(\frac{n}{2}+1)^{th} }{2} =\frac{2^{nd}+3^{rd}}{2} =\frac{63+63}{2}=\frac{126}{2}=63](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Cfrac%7Bn%7D%7B2%7D%29%5E%7Bth%7D%20%2B%28%5Cfrac%7Bn%7D%7B2%7D%2B1%29%5E%7Bth%7D%20%20%7D%7B2%7D%20%3D%5Cfrac%7B2%5E%7Bnd%7D%2B3%5E%7Brd%7D%7D%7B2%7D%20%3D%5Cfrac%7B63%2B63%7D%7B2%7D%3D%5Cfrac%7B126%7D%7B2%7D%3D63)
So, ![Q_3=63](https://tex.z-dn.net/?f=Q_3%3D63)
So, 75% of the heights of a team is less than 63 inches
Interquartile range = ![Q_3-Q_1=63-60=3](https://tex.z-dn.net/?f=Q_3-Q_1%3D63-60%3D3)
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.