Question

Below are the heights (in inches) of students in a third-grade class. Find the median height. 39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Answer 1

Given:

The heights (in inches) of students in a third-grade class are:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

To find:

The median height.

Solution:

The given data set is:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Arrange the data set in ascending order.

37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53

Here, the number of observations is 16. So, the median of the given data set is:

$Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}$

$Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}$

$Median=\dfrac{8\text{th term}+9\text{th term}}{2}$

$Median=\dfrac{47+48}{2}$

$Median=\dfrac{95}{2}$

$Median=47.5$

Therefore, the median height of the students is 47.5 inches.