Question

on a survey, 7 students reported how many minutes it takes them to travel to school. here are their responses. 13, 13, 3, 13, 10, 8, 16. find the mean travel time for these students. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n$ is the number of data points and $\sum_{i=1}^{n}x_i$ is the sum of the data points. Here, $n = 7$, and the data set is $x_1 = 13,x_2 = 13,x_3 = 3,x_4 = 13,x_5 = 10,x_6 = 8,x_7 = 16$.

Step2: Calculate the sum of data points

$\sum_{i = 1}^{7}x_i=13 + 13+3 + 13+10+8+16=(13\times3)+3 + 10+8+16=39+3 + 10+8+16=76$.

Step3: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{7}x_i}{7}=\frac{76}{7}\approx10.9$.

Answer:

$10.9$