Ezra counts the number of people who were 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?

Question

8,9,9,10,12,12,13,14,15,15,15,16,18,19,20

14
6
8
10

Answer 1

To find the interquartile range (IQR) of the dataset, we need to follow these steps:

1. Organize the Data: The data provided is already in ascending order: \[ 8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20 \]

2. Determine Quartiles:

   • Q1 (First Quartile): This is the median of the first half of the data.
   • Q2 (Median): This is the median of the entire dataset.
   • Q3 (Third Quartile): This is the median of the second half of the data.

   The dataset has 15 values, so:

   • The median (Q2) is the 8th value: \[ Q2 = 14 \]

   To find Q1, we take the first 7 values: \[ 8, 9, 9, 10, 12, 12, 13 \]

   • The median of this subset (the 4th value) is: \[ Q1 = 10 \]

   To find Q3, we take the last 7 values: \[ 15, 15, 15, 16, 18, 19, 20 \]

   • The median of this subset (the 4th value) is: \[ Q3 = 16 \]

3. Calculate the Interquartile Range (IQR): \[ \text{IQR} = Q3 - Q1 = 16 - 10 = 6 \]

So, the interquartile range of the data is 6.