Question

use the following table to answer each question. monthly water bills jan feb mar apr may june july aug sept oct nov dec $x_1$ $x_2$ $x_3$ $x_4$ $x_5$ $x_6$ $x_7$ $x_8$ $x_9$ $x_{10}$ $x_{11}$ $x_{12}$ $40 $42 $40 $38 $48 $50 $58 $62 $56 $46 $44 $44 6. using sigma notation find the mean water bill for the entire year. round your answer to the nearest cent. 7. using sigma notation find the mean water bill for the first 6 months of the year. round your answer to the nearest cent. 8. using sigma notation find the mean water bill from april through november. round your answer to the nearest cent.

Explanation:

Step1: Recall the formula for the mean

The mean $\bar{x}$ of a set of data $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i$.

Step2: Calculate the mean water - bill for the entire year (Question 6)

Here, $n = 12$, and $\sum_{i=1}^{12}x_i=40 + 42+40+38+48+50+58+62+56+46+44+44=568$.
The mean $\bar{x}=\frac{1}{12}\sum_{i = 1}^{12}x_i=\frac{568}{12}\approx47.33$.

Step3: Calculate the mean water - bill for the first 6 months (Question 7)

Here, $n = 6$, and $\sum_{i = 1}^{6}x_i=40+42 + 40+38+48+50=258$.
The mean $\bar{x}=\frac{1}{6}\sum_{i = 1}^{6}x_i=\frac{258}{6}=43.00$.

Step4: Calculate the mean water - bill from April through November (Question 8)

Here, $n = 8$, and the months are April ($x_4$) through November ($x_{11}$).
$\sum_{i = 4}^{11}x_i=38+48+50+58+62+56+46+44=402$.
The mean $\bar{x}=\frac{1}{8}\sum_{i = 4}^{11}x_i=\frac{402}{8}=50.25$.

Answer:

1. $\$47.33$
2. $\$43.00$
3. $\$50.25$