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
