Question

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: Find sum for question 11

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

Step2: Calculate average for question 11

$\frac{1}{9}\sum_{i = 1}^{9}x_i=\frac{658}{9}\approx73.11$
Rounding to nearest dollar gives $73$.
Interpretation: The average monthly cable - bill for the 9 - month period is approximately $\$73$.

Step3: Find sum for question 12

For $i$ from 1 to 4, $x_1 = 65,x_2 = 70,x_3 = 84,x_4 = 76$
$\sum_{i = 1}^{4}x_i=65 + 70+84 + 76=295$

Step4: Calculate average for question 12

$\frac{1}{4}\sum_{i = 1}^{4}x_i=\frac{295}{4}=73.75$
Rounding to nearest dollar gives $74$.
Interpretation: The average monthly cable - bill for the first 4 months (September - December) is approximately $\$74$.

Step5: Write formula for question 13

The second - semester months starting in February are February, March, April, May. So $n = 4$, and the formula for the mean is $\bar{x}=\frac{1}{4}\sum_{i = 6}^{9}x_i$, where $x_6 = 80,x_7 = 78,x_8 = 78,x_9 = 67$.
$\sum_{i = 6}^{9}x_i=80 + 78+78+67=303$
$\bar{x}=\frac{303}{4}=75.75\approx76$

Answer:

1. $73$
2. $74$
3. $\frac{1}{4}\sum_{i = 6}^{9}x_i\approx76$