Question

7 8 8 5 9 9 10 12 14 14 15 16 16
sonia and 11 of her classmates worked on a class fund - raiser. the list above shows the number of hours each
of these 12 students worked. exactly half of these students worked fewer hours than sonia. how many hours
did sonia work?
o 8
o 10
o 11
o 12

Explanation:

Step1: Arrange the data in ascending order

The data is already in ascending order: \(7,8,8,9,9,10,12,14,14,15,16,16\)

Step2: Find the median

Since \(n = 12\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=6\) and \(\frac{n}{2}+1 = 7\). The \(6\)th value is \(10\) and the \(7\)th value is \(12\). But we want the value such that exactly half of the students worked fewer hours than Sonia. For a set of \(n = 12\) data - points, the position we are interested in is the \(7\)th value (when we want to have \(6\) values less than a particular value).

Answer:

\(12\)