Question

the data set represents the total number of tickets each person purchased for a play.
0, 0, 1, 1, 1, 2, 2, 2, 4, 4
what is the median of the data?
1.5
2
1
2.5

Explanation:

Step1: Determine the number of data points

The data set is \(0, 0, 1, 1, 1, 2, 2, 2, 4, 4\). The number of data points \(n = 10\), which is even.

Step2: Find the two middle values

For an even number of data points, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values.
\(\frac{n}{2}=\frac{10}{2} = 5\)-th value and \((\frac{n}{2}+1)=6\)-th value.
Looking at the ordered data set:
1st: \(0\), 2nd: \(0\), 3rd: \(1\), 4th: \(1\), 5th: \(1\), 6th: \(2\), 7th: \(2\), 8th: \(2\), 9th: \(4\), 10th: \(4\).
The 5th value is \(1\) and the 6th value is \(2\).

Step3: Calculate the median

The median is the average of these two middle values. So, median \(=\frac{1 + 2}{2}=\frac{3}{2}=1.5\).

Answer:

\(1.5\)