Question

a group of 8 students was asked, \how many hours did you watch television last week?\ here are their responses.
18, 9, 12, 13, 8, 19, 14, 4
find the median and mean number of hours for these students.
if necessary, round your answers to the nearest tenth.
(a) median: hours
(b) mean: hours

Explanation:

Step1: Sort the data

Sort the data set \(4,8,9,12,13,14,18,19\)

Step2: Calculate the median

Since there are \(n = 8\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values.
\(\frac{n}{2}=4\), \(\frac{n}{2}+1 = 5\)
The \(4\)th value is \(12\) and the \(5\)th value is \(13\)
Median\(=\frac{12 + 13}{2}=\frac{25}{2}=12.5\)

Step3: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\)
\(\sum_{i=1}^{8}x_{i}=4 + 8+9+12+13+14+18+19=97\)
\(n = 8\)
Mean\(\bar{x}=\frac{97}{8}=12.125\approx12.1\)

Answer:

(a) Median: \(12.5\) hours
(b) Mean: \(12.1\) hours