At soccer practice, Mike asked each of his teammates to write down their shoe size.

Question

Shoe sizes
2
4
6
8
10
12
What is the interquartile range for Mike's teammates' shoe sizes?
sizes

Answer 1

To find the interquartile range (IQR) of the shoe sizes, we first need to arrange the sizes in ascending order and then find the first quartile (Q1) and the third quartile (Q3).

The shoe sizes are:

2, 4, 6, 8, 10, 12

1. Ordering the shoe sizes: The sizes are already in order: 2, 4, 6, 8, 10, 12.

2. Finding Q1 (first quartile):

   • The first quartile (Q1) is the median of the first half of the data (the lower half).
   • The lower half of the data is: 2, 4, 6.
   • The median of this is 4 (since it is the middle value).

3. Finding Q3 (third quartile):

   • The third quartile (Q3) is the median of the second half of the data (the upper half).
   • The upper half of the data is: 8, 10, 12.
   • The median of this is 10 (since it is the middle value).

4. Calculating the IQR: \[ \text{IQR} = Q3 - Q1 = 10 - 4 = 6 \]

Therefore, the interquartile range for Mike's teammates' shoe sizes is 6.