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AQA GCSE · Question 18.1 · Statistics
Two types of battery, P and Q, were tested. 100 of each type were put into clocks. The number of days each battery lasted was recorded.
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The frequency table represents the results for type P.
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On the grid, draw a cumulative frequency diagram to represent the data.
Two types of battery, P and Q, were tested. 100 of each type were put into clocks. The number of days each battery lasted was recorded.
<br>
The frequency table represents the results for type P.
<br>
On the grid, draw a cumulative frequency diagram to represent the data.
How to approach this question
1. Add a new column to the frequency table for "Cumulative Frequency".
2. Calculate the cumulative frequency for each row by adding the current row's frequency to the previous cumulative frequency. The first one is just the first frequency. The last one should equal the total number of items (100).
3. For a cumulative frequency graph, you plot points at the **upper boundary** of each class interval.
4. The points to plot will be (40, 2), (80, 11), (120, 37), etc.
5. Start the graph at the lowest possible value, which is (0, 0).
6. Join the plotted points with a smooth curve or straight lines.
Full Answer
To draw a cumulative frequency diagram, we first need to calculate the cumulative frequencies.
| Number of days, d | Frequency | Cumulative Frequency |
|-------------------|-----------|----------------------|
| 0 ≤ d < 40 | 2 | 2 |
| 40 ≤ d < 80 | 9 | 2 + 9 = 11 |
| 80 ≤ d < 120 | 26 | 11 + 26 = 37 |
| 120 ≤ d < 160 | 45 | 37 + 45 = 82 |
| 160 ≤ d < 200 | 18 | 82 + 18 = 100 |
We plot the cumulative frequency against the **upper bound** of each class interval.
The points to plot are:
(40, 2)
(80, 11)
(120, 37)
(160, 82)
(200, 100)
We should also start the curve from the lowest possible value, which is (0, 0).
Then, we join these points with a smooth curve.
A cumulative frequency diagram shows the running total of the frequencies.
First, we create a cumulative frequency column in the table:
- For d < 40, the frequency is 2. Cumulative frequency = 2.
- For d < 80, we add the next frequency: 2 + 9 = 11.
- For d < 120, we add the next frequency: 11 + 26 = 37.
- For d < 160, we add the next frequency: 37 + 45 = 82.
- For d < 200, we add the final frequency: 82 + 18 = 100. (This should match the total number of batteries).
Next, we plot these cumulative frequencies against the upper bound of each interval. The graph should start at (0, 0) because there are 0 batteries that lasted less than 0 days.
The points to plot are:
(0, 0)
(40, 2)
(80, 11)
(120, 37)
(160, 82)
(200, 100)
Finally, we connect these points with a smooth curve to create the cumulative frequency diagram.
Common mistakes
✗ Plotting frequencies instead of cumulative frequencies.
✗ Plotting points at the midpoint of the class intervals instead of the upper boundary.
✗ Not starting the curve at (0, 0).
✗ Drawing a bar chart instead of a line graph/curve.
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