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Mean, Median, and Mode

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Mean, Median, and Mode

Study Guide

Key Definition

The $\text{mean}$ of a set of numbers is the sum of the numbers divided by the total number of values. For example, the mean of the set $\{2, 5, 5, 6, 8, 8, 9, 11\}$ is $\frac{54}{8} = 6.75$. The $\text{median}$ is the middle value after ordering the data (or the average of the two middle values for an even-sized set). The $\text{mode}$ is the most frequently occurring value in the data set.

Important Notes

To find the $\text{mean}$, add all numbers and divide by their count.
The mean is sensitive to extreme values or outliers.
Mean is one measure of central tendency.
You may encounter mean in everyday statistics.
Practice calculating mean with real data sets.
To find the $\text{median}$, order the values and find the middle value (or average the two middle values for even counts).
To find the $\text{mode}$, identify the most frequent value(s) in the data set.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$\frac{a}{b}$ represents a fraction

Remember to use proper notation when solving problems

Why It Works

The mean provides a useful measure of the central value of a data set, effectively averaging out the values. The median shows the middle point and is resistant to extreme outliers. The mode indicates the most common value and can highlight frequent occurrences.

Remember

To calculate the mean, always sum up the data and divide by the number of data points.

Quick Reference

Mean Formula:$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

Median Formula:$\text{Median} = \text{Middle value (average of two middle values if necessary)}$

Mode Definition:$\text{Mode} = \text{Value(s) that appear most frequently}$

Understanding Mean, Median, and Mode

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The mean is the average of a set of numbers: add them up and divide by the count. The median is the middle value of an ordered list (or the average of the two middle values if there is an even number of entries). The mode is the value that appears most often.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Find the mean of the set $\{2, 5, 5, 6, 8, 8, 9, 11\}$.

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Suppose you have scored $70$, $75$, $80$, and $85$ in four different tests. What is your average score?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the data set $\{3, 7, 7, 7, 10, 15\}$. What impact does the number $15$ have on the mean?

Challenge Quiz

Single Choice Quiz

Advanced

If the mean of the numbers $\{x, 6, 8, 10\}$ is $8$, what is the value of $x$?

Recap

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Review key concepts and takeaways