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 country’s college tuitions? $53,270 $53,792 $53,846 $53,994 $51,454 $53,475 $50,883 $53,846 $53,966 $51,085
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.)
the midrange of the data set is $. (type an integer or decimal rounded to two decimal places as needed.)
the median of the data set is $. (type an integer or decimal rounded to two decimal places as needed.)
what is (are) the mode(s) of the data set?
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the mode(s) of the data set is (are) $. (type an integer or a decimal. do not round. use a comma to separate answers as needed.)
b. there is no mode.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $x_{i}$ are the data - points.
$\sum_{i=1}^{10}x_{i}=53270 + 53792+53846+53994+51454+53475+50883+53846+53966+51085=525611$
$\bar{x}=\frac{525611}{10}=52561.10$

Step2: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Max}+\text{Min}}{2}$.
The maximum value $\text{Max}=53994$ and the minimum value $\text{Min}=50883$.
Mid - range $=\frac{53994 + 50883}{2}=\frac{104877}{2}=52438.50$

Step3: Calculate the median

First, order the data: $50883,51085,51454,53270,53475,53792,53846,53846,53966,53994$.
Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points.
The $\frac{n}{2}=5$th value is $53475$ and the $(\frac{n}{2}+1)=6$th value is $53792$.
Median $=\frac{53475 + 53792}{2}=\frac{107267}{2}=53633.50$

Step4: Calculate the mode

The mode is the value that appears most frequently in the data set. The value $53846$ appears twice, and all other values appear only once. So the mode is $53846$.

Answer:

The mean of the data set is $\$52561.10$.
The midrange of the data set is $\$52438.50$.
The median of the data set is $\$53633.50$.
A. The mode(s) of the data set is (are) $\$53846$.