ExpertMedium3 marksStructured
AQA GCSE · Question 02 · Statistics
Here is a grouped frequency table.
<br>
<br>
Work out an estimate of the mean value.
Here is a grouped frequency table.
<br>
<br>
Work out an estimate of the mean value.
How to approach this question
1. Add a new column to the table for 'Midpoint × Frequency'.
2. For each row, calculate the product of the midpoint and the frequency.
3. Sum the values in this new column.
4. Sum the frequencies (the total is given as 60).
5. Divide the total of the 'Midpoint × Frequency' column by the total frequency.
Full Answer
To estimate the mean from a grouped frequency table, we follow these steps:
1. Find the midpoint of each class interval.
2. Multiply each midpoint by its corresponding frequency.
3. Sum the results from step 2 (Σfx).
4. Sum the frequencies (Σf).
5. Divide the sum of (midpoint × frequency) by the total frequency.
The table with calculations:
| Value, v | Frequency (f) | Midpoint (x) | f × x |
|---------------|---------------|--------------|----------------|
| 0 < v ≤ 10 | 16 | 5 | 16 × 5 = 80 |
| 10 < v ≤ 20 | 22 | 15 | 22 × 15 = 330 |
| 20 < v ≤ 30 | 13 | 25 | 13 × 25 = 325 |
| 30 < v ≤ 40 | 9 | 35 | 9 × 35 = 315 |
| **Total** | **Σf = 60** | | **Σfx = 1050** |
Sum of (midpoint × frequency) = 80 + 330 + 325 + 315 = 1050
Total frequency = 60
Estimated Mean = Σfx / Σf = 1050 / 60 = 17.5
**Answer: 17.5**
The mean of a set of data is the sum of the values divided by the number of values. For grouped data, we don't know the exact values, so we use the midpoint of each group as an estimate for all the values in that group.
First, we find the product of the midpoint and frequency for each group:
5 × 16 = 80
15 × 22 = 330
25 × 13 = 325
35 × 9 = 315
Next, we sum these products: 80 + 330 + 325 + 315 = 1050. This is our estimate for the total sum of all values.
The total number of values is the sum of the frequencies, which is 60.
Finally, we divide the total sum by the number of values: 1050 ÷ 60 = 17.5.
Common mistakes
✗ Dividing the sum of midpoints by the number of groups ( (5+15+25+35)/4 ). This ignores the frequencies.
✗ Dividing the sum of (midpoint × frequency) by 4 instead of the total frequency.
✗ Making calculation errors when multiplying or adding.
Practice the full AQA GCSE Maths Higher Tier Paper 2 Calculator
33 questions · hints · full answers · grading
More questions from this exam
Q01.1Choose a word from the list below to complete the sentence.
<br>
<br>
arc, centre, ci...EasyQ01.2Choose a word from the list below to complete the sentence.
<br>
<br>
arc, centre, ci...EasyQ01.3Choose a word from the list below to complete the sentence.
<br>
<br>
arc, centre, ci...EasyQ03In the grid below, shade one quarter of the squares so that the grid has exactly two lines of sym...EasyQ04A map has a scale of 1 : 4000
<br>
On the map, the distance from a station to a museum is...Medium