Question

a group of 6 students was asked, \how many hours did you watch television last week?\ here are their responses.
6, 5, 20, 20, 15, 19
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 \(5,6,15,19,20,20\).

Step2: Calculate the median

Since there are \(n = 6\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{6}{2}=3\) and \(\frac{6}{2}+1 = 4\). The 3rd value is \(15\) and the 4th value is \(19\). Median \(=\frac{15 + 19}{2}=\frac{34}{2}=17\).

Step3: Calculate the mean

Mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n = 6\). \(\sum_{i=1}^{6}x_{i}=5 + 6+15+19+20+20=85\). Mean \(=\frac{85}{6}\approx14.2\).

Answer:

(a) Median: \(17\) hours
(b) Mean: \(14.2\) hours