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The table shows some information about the profit made each day at a cricket club on 100 days - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 1
Question 11
The table shows some information about the profit made each day at a cricket club on 100 days. Profit (£) | Frequency ---|--- 0 ≤ x < 50 | 10 50 ≤ x < 100 | 15 100 ... show full transcript
Worked Solution & Example Answer:The table shows some information about the profit made each day at a cricket club on 100 days - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 1
Step 1
Complete the cumulative frequency table.
Answer
To complete the cumulative frequency table, we need to add the frequencies cumulatively:
- For the interval 0 ≤ x < 50, the cumulative frequency is 10.
- For the interval 50 ≤ x < 100, we add 15 to the previous total: 10 + 15 = 25.
- For the interval 100 ≤ x < 150, we add 25: 25 + 25 = 50.
- For the interval 150 ≤ x < 200, we add 30: 50 + 30 = 80.
- For the interval 200 ≤ x < 250, we add 15: 80 + 15 = 95.
- For the last interval 250 ≤ x < 300, we add the remaining frequency to reach the total of 100 days: 95 + 5 = 100.
Step 2
On the grid, draw a cumulative frequency graph for this information.
Answer
To draw the cumulative frequency graph:
- Plot the points based on the cumulative frequencies obtained:
- (0, 10)
- (50, 25)
- (100, 50)
- (150, 80)
- (200, 95)
- (250, 100)
- Connect the points with a smooth curve to represent the cumulative frequency distribution.
Step 3
Use your graph to find an estimate for the number of days on which the profit was less than £125.
Answer
From the graph, locate the point where the profit is £125. From the graph, find the corresponding cumulative frequency, which should be around 50 days (as per the earlier calculations).
Step 4
Use your graph to find an estimate for the interquartile range.
Answer
To find the interquartile range (IQR) using the graph:
-
Determine the first quartile (Q1) value where 25% of 100 days is located, hence find the point at a cumulative frequency of 25.
-
Determine the third quartile (Q3) value for 75% of 100 days, which corresponds to a cumulative frequency of 75.
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If Q1 is approximately £100 and Q3 is approximately £200, then the interquartile range is calculated as: