Question

1. write the formula for the mean cell phone bill for the last six months of the year using sigma notation and determine that mean. round your answer to the nearest cent.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a set of $n$ values $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i$. Here $n = 6$, and let the cell - phone bills for the last six months be $x_1,x_2,x_3,x_4,x_5,x_6$. So the formula for the mean is $\bar{x}=\frac{1}{6}\sum_{i = 1}^{6}x_i$.

Step2: Assume values (for example)

Suppose the bills for the six months are $x_1 = 50$, $x_2=55$, $x_3 = 60$, $x_4=58$, $x_5 = 62$, $x_6=53$. Then $\sum_{i = 1}^{6}x_i=50 + 55+60+58+62+53=338$.

Step3: Calculate the mean

$\bar{x}=\frac{1}{6}\times338\approx56.33$.

Answer:

The formula for the mean is $\frac{1}{6}\sum_{i = 1}^{6}x_i$ and the mean (using example values) is approximately $\$56.33$.