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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 sum the frequencies progressively:
- For 0 ≤ x < 50: Cumulative Frequency = 10
- For 0 ≤ x < 100: Cumulative Frequency = 10 + 15 = 25
- For 0 ≤ x < 150: Cumulative Frequency = 25 + 25 = 50
- For 0 ≤ x < 200: Cumulative Frequency = 50 + 30 = 80
- For 0 ≤ x < 250: Cumulative Frequency = 80 + 15 = 95
- For 0 ≤ x < 300: Cumulative Frequency = 95 + 15 = 100
Thus, the completed cumulative frequency table is:
Profit (£) Cumulative frequency
0 ≤ x < 50 10 0 ≤ x < 100 25 0 ≤ x < 150 50 0 ≤ x < 200 80 0 ≤ x < 250 95 0 ≤ x < 300 100
Step 2
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 cumulative frequency graph, locate the value where profit is £125 on the x-axis and draw a vertical line until it meets the graph. Read the corresponding cumulative frequency value on the y-axis, which should provide the estimate of days. The estimated number of days is approximately 50.
Step 4
Use your graph to find an estimate for the interquartile range.
Answer
To find the interquartile range (IQR), locate the first quartile (Q1) and third quartile (Q3) from the graph. Q1 corresponds to the cumulative frequency of 25 (which is around £75) and Q3 corresponds to the cumulative frequency of 75 (which is around £200).
The interquartile range can be calculated as:
IQR = Q3 - Q1 = 200 - 75 = 125.
Thus, the estimated interquartile range is £125.