Answer:
9
Step-by-step explanation:
To find the interquartile range (IQR) of the number of runs scored by the baseball team, we first need to find the first quartile (Q1) and the third quartile (Q3).
Given the data:
0, 1, 1, 3, 5, 6, 7, 7, 8, 9, 9, 12, 12, 15, 16
Find the Median (Q2):
Since there are an odd number of data points (15), the median (Q2) is the value at the middle position, which is the 8th value.
Median: (n+1)/2 th term = (15+1)/2 th term = 16/2 = 8th term
In the data set
0, 1, 1, 3, 5, 6, 7, 7(8th term), 8, 9, 9, 12, 12, 15, 16
The eight term is 7.
So,
Median (Q2) = 7
Split the Data into Lower and Upper Halves:
Lower half: 0, 1, 1, 3, 5, 6, 7
Upper half: 8, 9, 9, 12, 12, 15, 16
Find the Median of the Lower Half (Q1):
Since there are 7 data points in the lower half, the median of the lower half (Q1) is the value at the middle position, which is the 4th value.
Lower half: 0, 1, 1, 3(median), 5, 6, 7
So,
Q1 = 3
Find the Median of the Upper Half (Q3):
Since there are 7 data points in the upper half, the median of the upper half (Q3) is the value at the middle position, which is the 4th value.
Upper half: 8, 9, 9, 12(median), 12, 15, 16
So,
Q3 = 12
Calculate the Interquartile Range (IQR):
IQR = Q3 - Q1
= 12 - 3
= 9
Therefore, the interquartile range (IQR) of the number of runs scored by the baseball team is 9.
