Question

listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. what does this \top 10\ list tell us about the population of all of that countrys college tuitions? $54,393 $52,491 $53,353 $53,909 $53,578 $50,623 $54,053 $51,840 $52,037 $53,909
find the mean, midrange, median, and mode of the data set.
the mean of the data set is $
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points. Here $n = 10$, and the data points are $x_1=54393$, $x_2 = 52491$, $x_3=53353$, $x_4=53909$, $x_5=53578$, $x_6=50623$, $x_7=54053$, $x_8=51840$, $x_9=52037$, $x_{10}=53909$.

Step2: Calculate the sum of data - points

$\sum_{i = 1}^{10}x_{i}=54393 + 52491+53353+53909+53578+50623+54053+51840+52037+53909=530186$.

Step3: Calculate the mean

$\bar{x}=\frac{530186}{10}=53018.60$.

Step4: Recall mid - range formula

The mid - range $MR=\frac{\text{Max}+\text{Min}}{2}$. The maximum value $\text{Max}=54393$ and the minimum value $\text{Min}=50623$.

Step5: Calculate the mid - range

$MR=\frac{54393 + 50623}{2}=\frac{105016}{2}=52508$.

Step6: Recall median formula for $n = 10$ (even number of data - points)

First, order the data: $50623,51840,52037,52491,53353,53578,53909,53909,54053,54393$. The median $M=\frac{\text{the }(\frac{n}{2})\text{-th value}+\text{the }(\frac{n}{2}+1)\text{-th value}}{2}$. Here, $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. So $M=\frac{53353+53578}{2}=\frac{106931}{2}=53465.5$.

Step7: Recall mode formula

The mode is the value that appears most frequently in the data - set. The value $53909$ appears twice, and all other values appear once. So the mode is $53909$.

Answer:

The mean of the data set is $\$53018.60$.
The mid - range of the data set is $\$52508$.
The median of the data set is $\$53465.50$.
The mode of the data set is $\$53909$.