Question

the number of walkers sponsored by 80 teachers is summarized in the frequency bar - graph below. each teacher sponsored 1,2,3,4, or 5 walkers. what is the mean number of walkers who were sponsored by each teacher?

Explanation:

Step1: Recall mean formula

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$, where $x_{i}$ is the value and $f_{i}$ is the frequency.

Step2: Calculate $\sum_{i = 1}^{n}x_{i}f_{i}$

$x_1 = 1,f_1=10;x_2 = 2,f_2 = 15;x_3=3,f_3 = 30;x_4 = 4,f_4=20;x_5 = 5,f_5 = 5$. Then $\sum_{i = 1}^{5}x_{i}f_{i}=1\times10 + 2\times15+3\times30 + 4\times20+5\times5=10 + 30+90 + 80+25=235$.

Step3: Calculate $\sum_{i = 1}^{n}f_{i}$

$\sum_{i = 1}^{5}f_{i}=10 + 15+30+20 + 5=80$.

Step4: Calculate the mean

$\bar{x}=\frac{235}{80}=2.9375$.

Answer:

$2.9375$