How to Calculate the Mean, Median, Mode, and Range
🎬 Video: Mean, Median, Mode, and Range
How to Find the Mean? (0:01)
Definition: Mean, or Arithmetic Mean, tells you the average value of a set of numbers.
Formula: You calculate the mean by dividing the sum of all values by the total number of values:
$$ \text{Mean} = \frac{ \text{Sum of all values}}{\text{Total number of values}} $$
Example: Imagine your scores in archery are: 5, 7, 6, 3, 5. To find your average score, you can calculate the mean:
- Step 1: Add up all the scores: $$5 + 7 + 6 + 3 + 5 = 26 $$
- Step 2: Divide by the total number of shots
$$ \text{Mean} = \frac{5 + 7 + 6 + 3 + 5}{5} = \frac{26}{5} = 5.2 $$
- This means, on average, your archery score is 5.2.
How to Find the Median? (0:56)
The median is the value in the middle after sorting the numbers from smallest to largest.
💡 If the number of values is odd, the middle number is the median.
- Example: Scores after sorting = 3, 5, 5, 6, 7
- Here, 5 is in the middle, so Median = 5
💡If the number of values is even, take the average of the two middle numbers.
- Example: Scores after sorting = 3, 5, 5, 6, 7, 7
- The middle numbers are 5 and 6. To find their average, add them and divide by 2:
$$ \text{Median} = \frac{5 + 6}{2} = \frac{11}{2} = 5.5 $$
How to Locate the Median Position? (1:32)
To find the position of the median in an ordered data set, use the formula:
$$ \text{Median Position} = \frac{n + 1}{2} $$
Where $n$ is the total number of values. This formula is especially useful when there are many numbers in a data set.
Be careful: This gives you the position in the list, not the value itself!
- Example: Data set (already sorted): 2, 2, 2, 3, 4, 6, 6, 7, 9, 9
- There are 10 numbers, so:
$$ \text{Median Position} = \frac{10 + 1}{2} = \frac{11}{2} = 5.5 $$
- This means the median is halfway between the 5th and 6th values.
- The values at those positions are 4 (5th) and 6 (6th).
- Now calculate the median:
$$ \text{Median} = \frac{4 + 6}{2} = \frac{10}{2} = 5 $$
What is the Mode? (2:13)
The mode is the value that appears most often in a set of numbers.
- Example 1: Scores = 3, 5, 5, 6, 7
Here, 5 appears twice, while other numbers only appear once. So, Mode = 5 - Example 2: Scores = 3, 5, 5, 6, 7, 7
Here, 5 and 7 both appear twice, more than the others. So, Mode = 5 and 7
Exam tip: A data set can have one mode (if one number appears most often), more than one mode (if multiple numbers appear with the same highest frequency), or no mode at all (if no number repeats).
What is the Range? (2:35)
The range shows the spread of a data set. You find the range by subtracting the smallest value from the largest value:
$$ \text{Range} = \text{max value} \; – \; \text{min value} $$
- For example: 5, 7, 6, 3, 5
- Max value = 7
- Min value = 3
- So the Range is 7−3=4
💡 What the Range Tells You:
- A small range means the numbers are close together → The data is more consistent, and the results are steadier or more reliable.
- A large range means the numbers are spread out → The data is less consistent and shows more variation.
📂 Flashcards: How to Find Mean, Median, Mode, and Range
🍪 Quiz (6 Questions): Test Your Skills on Mean and Median
🎩 Struggling with Mean or Median? Try AI Math Solver
Need math help? Chat with our AI Math Solver at the bottom right — available 24/7 for instant answers.