Question

The following are the ages of 13 physics teachers in a school district,24, 27, 28, 28, 35, 38, 40, 46, 47, 53, 53, 57, 58Notice that the ages are ordered from least to greatest.Give the five-number summary and the interquartile range for the data set.Five-number summaryMinimum:Lower quartile:Median:Upper quartile: .Maximum: 0Interquartile range:

Answer 1

The median is placed in the middle of the ordered list. Given there are 13 values, the middle is at 7th place.

To find the lower quartile (Q1) we need to consider the first half of values. Given there are 6 values, the middle is between the 3rd and 4th places (the average of these two values is taken).

To find the upper quartile (Q3) we need to consider the second half of values. Given there are 6 values, the middle is between the 10th and 11th places (the average of these two values is taken).

Interquartile range (IQR) is calculated as follows:

`\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \text{IQR}=53-28 \\ \text{IQR}=25 \end{gathered}`

Five-number summary

• Minimum: 24

,

• Lower quartile: 28

,

• Median: 40

,

• Upper quartile: 53

,

• Maximum: 58

,

• Interquartile range: 25