Respuesta :
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 [tex](Q_1)[/tex]
For a set of data, a number for which 75% of the data is less than that number is known as the third quartile [tex](Q_3)[/tex]
Terms in arranged in ascending order:
[tex]57,60,60,61,62,62,63,63,64[/tex]
Number of terms = 9
As number of terms is odd, exclude the middle term that is 62.
[tex]Q_1[/tex] is median of terms [tex]57,60,60,61[/tex]
Number of terms (n) = 4
Median = [tex]\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[/tex]
So, [tex]Q_1=60[/tex]
So, 25% of the heights of a team is less than 60 inches
[tex]Q_3[/tex] is the median of terms [tex]62,63,63,64[/tex]
Median = [tex]\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[/tex]
So, [tex]Q_3=63[/tex]
So, 75% of the heights of a team is less than 63 inches
Interquartile range = [tex]Q_3-Q_1=63-60=3[/tex]
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.
