Question

before the last school year began, it was estimated that the average discretionary personal expenses each school - year for a student attending a 4 - year public college were $2,110. this past summer ashley decided to poll seven of her friends attending a 4 - year public college because she thought that estimate was low. she made a list of their actual school - year expenses: $1,800 $1,900 $2,005 $2,400 $1,860 $2,200 $2,000. a. what is the mean of her friends personal expenses? round your answer to the nearest cent. b. how does that average compare with the estimate? c. what would ashleys actual personal expenses for that school year have to be so that her amount and her friends amounts together would have an average of $2,110?

Explanation:

Step1: Calculate the sum of expenses

$1800 + 1990+2005 + 2400+1860+2200+2000=14255$

Step2: Calculate the mean

The number of data - points $n = 7$. Mean $\bar{x}=\frac{14255}{7}\approx2036.43$

Step3: Compare with the estimate

The estimate was $2110$. Since $2036.43<2110$, the mean of her friends' expenses is less than the estimate.

Step4: Find Ashley's expense for a certain average

Let Ashley's expense be $x$. There are $n = 8$ people in total. We want the average $\bar{y}=2110$. Using the average formula $\bar{y}=\frac{14255 + x}{8}$. Then $2110\times8=14255 + x$. So $x=2110\times8 - 14255=16880 - 14255 = 2625$

Answer:

a. $\$2036.43$
b. The mean of her friends' expenses ($\$2036.43$) is less than the estimate of $\$2110$.
c. $\$2625$