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The histogram shows information about the times taken by some students to finish a puzzle - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 2
Question 18
The histogram shows information about the times taken by some students to finish a puzzle. (a) Complete the frequency table for this information. | Time taken (n m... show full transcript
Worked Solution & Example Answer:The histogram shows information about the times taken by some students to finish a puzzle - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 2
Step 1
Complete the frequency table for this information
Answer
To complete the frequency table using the histogram:
-
Calculate the frequencies for each interval.
- For the interval 0 < n ≤ 5 (width = 5):
- Height of the histogram: 0.8 → Frequency = 0.8 * 5 = 4
- For the interval 5 < n ≤ 15 (width = 10):
- Height of the histogram: 0.6 → Frequency = 0.6 * 10 = 6
- For the interval 15 < n ≤ 25 (width = 10):
- Height of the histogram: 0.8 → Frequency = 0.8 * 10 = 8
- For the interval 25 < n ≤ 30 (width = 5):
- Height of the histogram: 0.4 → Frequency = 0.4 * 5 = 2
- For the interval 30 < n ≤ 50 (width = 20):
- Height of the histogram: 0.2 → Frequency = 0.2 * 20 = 4
- For the interval 0 < n ≤ 5 (width = 5):
-
Fill the frequency table with the calculated frequencies:
| Time taken (n minutes) | Frequency |
|---|---|
| 0 < n ≤ 5 | 4 |
| 5 < n ≤ 15 | 6 |
| 15 < n ≤ 25 | 8 |
| 25 < n ≤ 30 | 2 |
| 30 < n ≤ 50 | 4 |
Step 2
Find an estimate for the lower quartile of the times taken to finish the puzzle
Answer
To estimate the lower quartile (Q1), we typically find the value below which 25% of the data falls:
-
Calculate the total number of students:
- Total frequency = 4 + 6 + 8 + 2 + 4 = 24
-
Determine the position of the lower quartile:
- Q1 position = (1/4) * 24 = 6th value.
-
Identify which class the 6th value falls into by adding frequencies cumulatively:
- 0 < n ≤ 5: 4
- 5 < n ≤ 15: 4 + 6 = 10 (6th value falls here)
- 15 < n ≤ 25: 10 + 8 = 18 (not reached yet)
-
Estimate the lower quartile:
- Since Q1 falls in the interval 5 < n ≤ 15, we can estimate that Q1 is approximately at the lower end of this interval, which is 5 minutes.