Answer:
9.5
Step-by-step explanation:
The formula for interquartile range = Third Quartile - 1st Quartile
= Q3 - Q1
Looking at the histogram given, the class width = 6
Step 1
We find the number of values = n
n = 1 + 12 + 26 + 27 + 31 + 19 + 6 + 1
= 123
Frequency Cumulative Frequency
1 1
12 13
26 39
27 66
31 97
19 116
6 122
1 123
Step 2
We find Q1 ( First Quartile)
Q1 =1/4 (n + 1) value
Q1 = 1/4(124) value
= 31st value
The first Quartile = 31st value
31 - 13 = 18
31st value = 12 + (18/26 × class width)
= 12 +( 18/26 × 6)
First Quartile = 16.153846154
Third Quartile =Q3 =3/4 (n + 1) value
Q1 = 3/4(124) value
= 93rd value
The first Quartile = 93rd value
93 - 66 = 27
93rd value = 1 + (27/97 × class width)
=24 +( 27/97 × 6)
Third Quartile= 25.670103093
Interquartile range = Q3 - Q1
= 25.670103093 - 16.153846154
= 9.5162569392
Approximately = 9.5
Inter Quartile range = 9.5
