Question

a group of 8 students was asked, \how many hours did you watch television last week?\ here are their responses. 20, 6, 10, 6, 14, 12, 10, 4 find the mean and median number of hours for these students. if necessary, round your answers to the nearest tenth. (a) mean: hours (b) median: hours

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$ and $x=\{20,6,10,6,14,12,10,4\}$.
$\sum_{i=1}^{8}x_{i}=20 + 6+10+6+14+12+10+4=82$
$\bar{x}=\frac{82}{8}=10.25\approx10.3$

Step2: Calculate the median

First, sort the data set: $\{4,6,6,10,10,12,14,20\}$.
Since $n = 8$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
Here, $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. $x_{4}=10$ and $x_{5}=10$.
$M=\frac{10 + 10}{2}=10$

Answer:

(a) $10.3$ hours
(b) $10$ hours