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.
2. write the formula for the mean cell phone bill from march to september using sigma notation and determine that mean. round your answer to the nearest cent.
3. write the sigma notation mean formula for the three - consecutive month period that would have the highest mean of the year.

use the following table to answer questions 11 - 13.
jouen attends state university and lives in an on - campus dorm suite with five friends. they share the cost of the monthly upgraded cable bill for their suite. below is a listing of the bills for their freshman year.
monthly cable bill

sept	oct	nov	dec	jan	feb	mar	apr	may
$65	$70	$84	$76	$50	$80	$78	$78	$67

1. round the following value $\frac{1}{9}sum_{i = 1}^{9}x_i$ to the nearest dollar.

interpret the answer in the context of the problem.

1. round the following value $\frac{1}{4}sum_{i = 1}^{4}x_i$ to the nearest dollar.

interpret the answer in the context of the problem.

1. write the sigma notation mean formula for the second semester beginning in february and determine that semester average rounded to the nearest dollar.

Explanation:

Step1: Recall the mean formula

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

Step2: Calculate $\sum_{i=1}^{9}x_i$ for question 11

We have $x_1 = 65,x_2=70,x_3 = 84,x_4=76,x_5 = 50,x_6=80,x_7 = 78,x_8=78,x_9=67$. Then $\sum_{i = 1}^{9}x_i=65 + 70+84+76+50+80+78+78+67=658$.

Step3: Calculate the mean for question 11

$\frac{1}{9}\sum_{i = 1}^{9}x_i=\frac{658}{9}\approx73.11\approx73$. This represents the average monthly cable bill for the 9 - month period in dollars.

Step4: Calculate $\sum_{i = 1}^{4}x_i$ for question 12

Here, $x_1 = 65,x_2=70,x_3 = 84,x_4=76$. So $\sum_{i = 1}^{4}x_i=65 + 70+84+76=295$.

Step5: Calculate the mean for question 12

$\frac{1}{4}\sum_{i = 1}^{4}x_i=\frac{295}{4}=73.75\approx74$. This represents the average monthly cable bill for the first 4 - month period in dollars.

Step6: For question 13

The second - semester months starting from February are $x_6,x_7,x_8,x_9,x_5$ (assuming a non - standard academic year start). The mean formula is $\bar{x}=\frac{1}{5}\sum_{i = 6}^{10}x_i$ (where we consider $x_{10}=x_5$ for the 5 - month period). $\sum_{i = 6}^{10}x_i=80 + 78+78+67+50=353$.

Step7: Calculate the mean for question 13

$\frac{1}{5}\sum_{i = 6}^{10}x_i=\frac{353}{5}=70.6\approx71$.

Answer:

1. $73$; This is the average monthly cable bill for the 9 - month period.
2. $74$; This is the average monthly cable bill for the first 4 - month period.
3. The formula is $\frac{1}{5}\sum_{i = 6}^{10}x_i$ and the average is $71$.