Question

what is the median number of students?
median = students 5 5 7 7 7 8 8 10 10 10 10 11 11 11

Explanation:

Step1: Count the number of data points

There are \(n = 14\) data points.

Step2: Find the position of the median

For \(n\) even, the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+ 1)\) - th values. \(\frac{n}{2}=\frac{14}{2}=7\), \(\frac{n}{2}+1 = 8\).

Step3: Identify the 7 - th and 8 - th values

The ordered data set is \(5,5,7,7,7,8,8,10,10,10,10,11,11,11\). The 7 - th value is \(8\) and the 8 - th value is \(10\).

Step4: Calculate the median

Median \(=\frac{8 + 10}{2}=\frac{18}{2}=9\)

Answer:

\(9\)