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?
$ 54,268  $ 52,820  $ 54,298  $ 52,678  $ 52,319   
$ 52,561  $ 54,219  $ 52,820  $ 53,772  $ 50,963
Question content area bottom
Part 1
Find the​ mean, midrange,​ median, and mode of the data set.
The mean of the data set is ​$
  

​Round to two decimal places as​ needed.

Let's first calculate the required statistical measures: the mean, midrange, median, and mode of the given tuition amounts.

### 1. Mean
The mean is calculated by summing all the values and dividing by the number of values.

Given dataLet's first calculate the required statistical measures: the mean, midrange, median, and mode of the given tuition amounts.

### 1. Mean
The mean is calculated by summing all the values and dividing by the number of values.

Given 
\[
\text{Data Set} = \{54,268, 52,820, 54,298, 52,678, 52,319, 52,561, 54,219, 52,820, 53,772, 50,963\}
\]

Sum of the values:
\[
54,268 + 52,820 + 54,298 + 52,678 + 52,319 + 52,561 + 54,219 + 52,820 + 53,772 + 50,963 = 530,718
\]

Number of values:
\[
n = 10
\]

Mean:
\[
\text{Mean} = \frac{530,718}{10} = 53,071.80
\]

### 2. Midrange
The midrange is calculated as the average of the maximum and minimum values in the data set.

Minimum value:
\[
\text{Min} = 50,963
\]

Maximum value:
\[
\text{Max} = 54,298
\]

Midrange:
\[
\text{Midrange} = \frac{\text{Min} + \text{Max}}{2} = \frac{50,963 + 54,298}{2} = \frac{105,261}{2} = 52,630.50
\]

### 3. Median
The median is the middle value when the data set is ordered. Since there are 10 values, the median will be the average of the 5th and 6th values.

Ordered data set:
\[
50,963, 52,319, 52,561, 52,678, 52,820, 52,820, 53,772, 54,219, 54,268, 54,298
\]

Median:
\[
\text{Median} = \frac{52,820 + 52,820}{2} = 52,820
\]

### 4. Mode
The mode is the value that occurs most frequently in the data set.

In this case, the value **52,820** appears twice, so the mode is:
\[
\text{Mode} = 52,820
\]

### Summary of Results
- **Mean**: $ 53,071.80 $
- **Midrange**: $ 52,630.50 $
- **Median**: $ 52,820 $
- **Mode**: $ 52,820 $

---

This "Top 10" list provides insight into the higher end of the tuition spectrum but does not give a complete picture of the overall distribution of college tuition costs in the country. The measures suggest that tuition amounts among the most expensive colleges are relatively close, but they are likely not representative of the entire population of tuition costs, which could include much lower figures.

---

Would you like further details on any of these calculations? Here are some related questions:

1. How does the median compare to the mean in this data set?
2. What does the presence of a mode tell us about the data distribution?
3. How would the midrange change if we included lower-cost colleges?
4. What could be the potential effects of outliers on these statistics?
5. How would you interpret these results if more data points were available?

**Tip:** When analyzing data, it's crucial to understand whether the data set is representative of the entire population, especially when dealing with extreme values like top 10 lists.

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? $54,268 $52,820 $54,298 $52,678 $52,319 $52,561 $54,219 $52,820 $53,772 $50,963 Find the​ mean, midrange,​ median, and mode of the data set.

Explore how to calculate the mean, midrange, median, and mode of the 10 most expensive college tuitions in a country. Learn key statistical concepts and formulas in this detailed step-by-step solution. Suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation