What Is How to Find the Mean?
The mean is the sum of the values divided by how many there are. It is the number people usually mean by average, and it is the balance point of the data.
Choose to find the mean of a list, of a frequency table, or to find the next value you need to reach a target mean. Each mode shows the addition, the count and the division, with a working table and charts.
Below are the formulas, a worked example with five scores and answers on the target-average method.
How to Use the How to Find the Mean Calculator
- Choose list, frequency table or target.
- Enter the values.
- Follow the add-and-divide steps.
- Check the working table.
How to Find the Mean Formula
Mean
Mean from a frequency table
Next value for a target mean
How to Find the Mean Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Σx | Sum of the values | |
| n | Count of values | |
| f | Frequency | |
| T | Target mean |
How to Find the Mean Worked Example
The scores 72, 85, 90, 64, 78 add to 389, and there are 5 of them, so the mean is 389 ÷ 5 = 77.8. To reach a mean of 80 over 6 scores you need a total of 480, so the next score must be 480 − 389 = 91.
With the example values loaded in the calculator above, the steps are:
- Add all 5 values: 72 + 85 + 90 + 64 + 78 = 389.
- Count the values: n = 5.
- Mean = sum ÷ n = 389 ÷ 5 = 77.8.
Result: Mean = 77.8.
How to Read a Mean
The mean is the balance point of the data: the sum of all values divided by how many there are. The scores 72, 85, 90, 64 and 78 total 389, so the mean is 77.8. The table shows how far each score sits from that mean, and those distances always cancel to zero.
Because every value counts, a single extreme value pulls the mean toward it. If the data are skewed, the median may describe the typical value better. The target-mean mode answers a different question: the score you need next to reach a goal.
Where How to Find the Mean Is Used
Everyday averages
Find the mean of scores, prices or measurements from a list.
Frequency tables
Use values and their frequencies when the data come grouped, as in survey counts.
Target averages
Work out the score you need on the next test to reach a chosen mean.
Homework
Check your sum and your division against the calculator.
Common How to Find the Mean Mistakes to Avoid
- Count the values before dividing. A missed or doubled value changes the mean.
- In a frequency table, multiply each value by its frequency, then divide by the total frequency, not by the number of rows.
- To reach a target mean over n scores, you need a total of n × target. The next score is that total minus the sum so far.
- Report the mean with the same precision as your data. Do not show six decimals for whole-number scores.
How to Find the Mean Terms and Definitions
- Mean
- The sum of the values divided by the number of values.
How to Find the Mean FAQs
How do you find the mean?
Add all the values and divide by how many there are. For 72, 85, 90, 64 and 78 the sum is 389, and 389 ÷ 5 = 77.8.
How do I find the mean from a frequency table?
Multiply each value by its frequency, add those products, and divide by the sum of the frequencies. This is the same as writing out every repeated value.
What score do I need to reach a target average?
Multiply the target by the number of scores to get the total needed, then subtract the sum you already have. To average 80 over 6 scores you need 480, so the sixth score is 480 − 389 = 91.
Is the mean the same as the average?
In everyday use, yes. In statistics "average" can mean mean, median or mode, so say which one you are using.