All four ideas are ways to understand a set of numbers. They help us describe what the data is like: its center (middle) and how spread out it is.
Mean (the average)
What it is: The mean is the average value. Add all the numbers together and divide by how many numbers there are.
Formula: Mean = sum of all numbers ÷ number of values
Example dataset: 3, 7, 7, 2, 9
Calculation: Sum = 3 + 7 + 7 + 2 + 9 = 28
There are 5 numbers, so Mean = 28 ÷ 5 = 5.6
Median (the middle value)
What it is: The median is the middle number when the data are lined up from smallest to largest.
Steps:
- Sort the data: 2, 3, 7, 7, 9
- Choose the middle value: the 3rd number is 7
Median: 7
Mode (the most common value)
What it is: The mode is the number that appears most often.
Example: In 3, 7, 7, 2, 9, the number 7 appears twice, more than any other number.
Mode: 7
Note: A dataset can have more than one mode (multimodal) or no mode if all values are different.
Range (how spread out the data is)
What it is: The range tells you how far the smallest and largest values are from each other.
Formula: Range = max value − min value
Example: In the dataset 3, 7, 7, 2, 9, max = 9, min = 2
Range = 9 − 2 = 7
Putting it all together
For the dataset 3, 7, 7, 2, 9:
- Mean = 5.6
- Median = 7
- Mode = 7
- Range = 7
Connecting to probability
In probability, the mean is like the expected outcome after many trials. The median is less influenced by extreme results, and the range shows how much outcomes can vary.
Quick practice
Try another small dataset and calculate the four measures:
- Dataset: 1, 4, 4, 6, 9
- Mean: ?
- Median: ?
- Mode: ?
- Range: ?
Answers: Mean = (1+4+4+6+9) = 24; 24 ÷ 5 = 4.8; Median = 4; Mode = 4; Range = 9 − 1 = 8.