Question

1. 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: $2,800 $1,990 $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?

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 7$, and $x_1=2800$, $x_2 = 1990$, $x_3=2005$, $x_4 = 2400$, $x_5=1860$, $x_6=2200$, $x_7=2000$.

Step2: Calculate the sum of data - points

$\sum_{i = 1}^{7}x_{i}=2800 + 1990+2005+2400+1860+2200+2000=15255$.

Step3: Calculate the mean

$\bar{x}=\frac{15255}{7}\approx2179.29$.

Answer:

A. The mean of her friends' personal expenses is $\$2179.29$.
B. The estimated average discretionary personal expenses per school - year was $\$2110$, and the mean of her friends' expenses is $\$2179.29$. So the mean of her friends' expenses is higher than the estimate. The difference is $2179.29 - 2110=\$69.29$.