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Mean
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EasyQuestion 1
[2 marks]Find the mean of these numbers: 12, 15, 8, 19, 11
Solution for Question 1
MediumQuestion 2
[3 marks]The mean of five numbers is 24. Four of the numbers are 18, 27, 31, and 20.
Find the fifth number.
Solution for Question 2
HardQuestion 3
[5 marks]The table shows the number of goals scored by a football team in 30 matches.
| Goals (x) | 0 | 1 | 2 | 3 | 4 |
|-----------|---|---|---|---|---|
| Frequency (f) | 4 | 8 | 10 | 6 | 2 |
(a) Calculate the mean number of goals per match.
(b) The team plays one more match and scores 5 goals. Calculate the new mean.
Solution for Question 3
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Generate Unlimited QuestionsAbout Mean in AQA GCSE
The mean is the most commonly used average and is a key measure of central tendency in statistics. It represents the typical value in a dataset.
**Calculating the Mean:**
Mean = Sum of all values ÷ Number of values
Mean = Σx ÷ n
**From a List of Values:**
Add all values together and divide by how many there are.
Example: Mean of 4, 7, 9, 12, 8 = (4+7+9+12+8) ÷ 5 = 40 ÷ 5 = 8
**From a Frequency Table:**
Mean = Σ(x × f) ÷ Σf
1. Multiply each value by its frequency
2. Add all these products
3. Divide by the total frequency
**From Grouped Data:**
Use the midpoint of each class interval as x.
Mean = Σ(midpoint × f) ÷ Σf
**Finding a Missing Value:**
If you know the mean and most values, work backwards:
Sum = Mean × Number of values
Missing value = Sum - (sum of known values)
**Advantages and Disadvantages:**
✓ Uses all the data
✓ Easy to calculate
✗ Affected by extreme values (outliers)
✗ May not be a whole number
✗ May not be an actual data value
**Exam Tips:**
- Show your working clearly: sum ÷ count
- For grouped data, always use midpoints
- Check if your answer seems reasonable
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