Here’s an engaging explanation of the four main types of averages:The Fantastic Four Averages: Mean, Median, Mode, and RangeImagine you’re a detective trying to understand a group of numbers. These four averages are your trusty tools to uncover the story behind the data:

**Mean**(The Balancer)

The mean is like finding the balance point of all the numbers.

- Add up all the numbers
- Divide by how many numbers there are

It’s great for getting an overall sense, but can be thrown off by extreme values.

Example: Test scores: 80, 85, 90, 95, 100

Mean = (80 + 85 + 90 + 95 + 100) / 5 = 90

**Median**(The Middle Manager)

The median is the middle number when everything is in order.

- Arrange the numbers from smallest to largest
- Find the middle number (or average of two middle numbers)

It’s not affected by extreme values, so it’s good for data with outliers.

Example: House prices: $100k, $150k, $200k, $250k, $1 million

Median = $200k (the middle number)

**Mode**(The Popularity Contest Winner)

The mode is the most frequent number – the popular kid of the group.

- Count how many times each number appears
- The number that shows up most is the mode

It’s useful for finding the most common value, especially in non-numerical data.

Example: Favorite colors: Red, Blue, Green, Blue, Yellow, Blue

Mode = Blue (appears 3 times)

**Range**(The Stretch Armstrong)

The range shows how spread out the numbers are.

- Find the smallest and largest numbers
- Subtract the smallest from the largest

It gives you an idea of the data’s variability.

Example: Ages in a family: 5, 10, 15, 40, 42

Range = 42 – 5 = 37 years

**Remember:**

- Mean tells you the average.
- Median shows you the middle.
- Mode reveals what’s most common.
- Range indicates how spread out the data is.

By using all four, you get a well-rounded picture of your data set. Each average has its strengths, so choose the right tool for the job.

##### Here are some exercises to test your understanding of mean, median, mode and range:

## Mean:

- Find the mean of the following numbers: 12, 15, 18, 21, 24
- The test scores for 6 students are: 85, 92, 78, 90, 88, 95. What is the mean score?
- A bakery sold the following number of cupcakes each day for a week: 24, 36, 30, 42, 28, 38, 32. What was the mean number of cupcakes sold per day?

## Median:

- Find the median of this set of numbers: 7, 13, 3, 9, 5, 11
- What is the median of these test scores: 72, 85, 93, 68, 79, 88, 91?
- Order these numbers and find the median: 14, 22, 17, 19, 25, 20, 16, 23

## Mode:

- Find the mode of this data set: 5, 8, 3, 8, 6, 4, 8, 7, 3
- What is the mode of these shoe sizes: 7, 8, 6, 7, 9, 8, 7, 6, 8, 7?
- Determine the mode(s) for this set: 12, 15, 12, 18, 15, 20, 12, 18

## Range:

- Calculate the range of this data: 28, 35, 42, 39, 31, 44
- Find the range of these temperatures: 72°F, 68°F, 75°F, 70°F, 79°F, 73°F
- What is the range of these test scores: 88, 92, 85, 79, 94, 90, 83?

## Mixed Practice:

- For the data set 4, 7, 2, 9, 5, 7, 3, 7, find:

a) Mean

b) Median

c) Mode

d) Range - The heights (in inches) of 8 students are: 58, 62, 59, 61, 60, 62, 57, 60, calculate the:

a) Mean height

b) Median height

c) Mode height

d) Range of heights