ezra counts the number of passengers who are already on the bus when he gets on each morning. his data for…

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

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20.

Step2: Find the median (Q2)

There are (n = 15) data - points. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{15+1}{2}=8) - th value. So, (Q2=14).

Step3: Find the lower half and Q1

The lower half of the data is 8, 9, 9, 10, 12, 12, 13. There are (n_1 = 7) data - points. The median of the lower half (Q1) is the (\left(\frac{7 + 1}{2}\right))-th value. (\frac{7+1}{2}=4) - th value. So, (Q1 = 10).

Step4: Find the upper half and Q3

The upper half of the data is 15, 15, 15, 16, 18, 19, 20. There are (n_2 = 7) data - points. The median of the upper half (Q3) is the (\left(\frac{7+1}{2}\right))-th value. (\frac{7 + 1}{2}=4) - th value. So, (Q3 = 16).

Step5: Calculate the inter - quartile range (IQR)

(IQR=Q3 - Q1). Substitute (Q1 = 10) and (Q3 = 16) into the formula. (IQR=16 - 10=6).