Question

Ezra counts the number of passengers who are already on the bus when he gets on each morning. His data for the last 15 days are shown below. What is the interquartile range of the data?
8,9,9,10,12,12,13,14,15,15,15,16,18,19,20

Answer 1

To find the interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3).

1. Arrange the data in ascending order:
8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20

2. Find the median (Q2) of the entire data set:
Median (Q2) = (15 + 15) / 2 = 15

3. Find the median of the lower half of the data to get Q1:
Lower Half: 8, 9, 9, 10, 12, 12, 13, 14
Q1 = (10 + 12) / 2 = 11

4. Find the median of the upper half of the data to get Q3:
Upper Half: 15, 15, 15, 16, 18, 19, 20
Q3 = (15 + 18) / 2 = 16.5

5. Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 16.5 - 11
IQR = 5.5

Therefore, the interquartile range of the data is 5.5.