Mean (Edexcel GCSE Statistics): Revision Notes
Mean
Understanding the mean from frequency tables
When you have data organised in a frequency table, you need a special method to calculate the mean. This is different from finding the mean of a simple list of numbers because some values appear more frequently than others.
The key difference with frequency tables is that each value has a frequency - this tells us how many times that particular value appears in the dataset. We must account for this frequency when calculating the mean.
The mean from a frequency table uses this essential formula:
Let's break down what each part of this formula means:
- (x-bar) represents the mean of all the x-values
- is the sum of all the frequency values (how many times each value occurs)
- is the sum of all the f × x values (each value multiplied by its frequency)
Step-by-step method for calculating mean from frequency tables
Systematic Approach for Mean from Frequency Tables
Here's the method you should follow every time:
- Add an f × x column to your frequency table on the right-hand side
- Calculate each f × x value by multiplying each x-value by its corresponding frequency
- Find Σfx by adding up all the values in your f × x column
- Find Σf by adding up all the frequency values
- Apply the formula by dividing Σfx by Σf
This systematic approach ensures you don't miss any steps and helps prevent calculation errors. The f × x column is essential because it organises your work and makes the final calculation straightforward.
Worked example 1: European shoe sizes
Worked Example: Mean Shoe Size
Let's work through a complete example using data about shoe sizes of 20 people:
| Shoe size | Frequency | f × x |
|---|---|---|
| 28 | 8 | 8 × 28 = 224 |
| 30 | 7 | 7 × 30 = 210 |
| 32 | 3 | 3 × 32 = 96 |
| 34 | 2 | 2 × 34 = 68 |
| Totals | 20 | 598 |
Step-by-step calculation:
- (sum of all frequencies)
- (sum of all f × x values)
- Mean =
Therefore, the mean shoe size is 29.9.
Worked example 2: Number of letters in first names
Worked Example: Mean Number of Letters
This example shows information about the number of letters in the first names of 50 people:
| Number of letters | Frequency | f × x |
|---|---|---|
| 3 | 2 | 2 × 3 = 6 |
| 4 | 5 | 5 × 4 = 20 |
| 5 | 14 | 14 × 5 = 70 |
| 6 | 19 | 19 × 6 = 114 |
| 7 | 10 | 10 × 7 = 70 |
| Totals | 50 | 280 |
Step-by-step calculation:
- Mean =
The mean number of letters in the first names is 5.6 letters.
Common mistakes and exam tips
Watch Out for These Common Errors
Zero multiplication mistake: A very common error is writing 5 × 0 = 5 instead of 5 × 0 = 0. Always check your arithmetic carefully, especially when dealing with zero frequencies.
Missing the total frequency: Sometimes the question won't tell you the total frequency. In this case, you need to work it out yourself by adding up all the frequency values before you can use the formula.
Misunderstanding the mean: Remember that the mean from a frequency table gives you the average value taking into account how often each value appears. It's not just a simple average of the x-values.
Rounding errors: Always check how many decimal places the question asks for in your final answer, and round appropriately.
Understanding what your answer means is just as important as getting the calculation right. The mean represents the typical value when the frequency of each data point is considered.
Key Points to Remember:
- The formula for mean from frequency tables is:
- Always add an f × x column to help organise your calculations
- is the sum of all frequencies, and is the sum of all f × x values
- Check your arithmetic carefully, especially when multiplying by zero
- The mean takes into account how frequently each value occurs, not just the values themselves