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 minutes) Frequency 0 < n ≤ 5 4 5 < n ≤ 15 15 < n ≤ 25 25 < n ≤ 30 30 < n ≤ 50 (b) Find an estimate for the lower quartile of the times taken to finish the puzzle.

GCSE Edexcel Maths Volume, Area & Surface Area: The histogram shows information

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 min... 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.

96%

114 rated

Answer

To complete the frequency table, we need to calculate the frequencies based on the histogram data:

For the interval (0 < n ≤ 5), the histogram indicates a frequency density of approximately 0.8. The width of this interval is 5 minutes. Thus, the frequency is: $ext{Frequency} = ext{Density} \times \text{Width} = 0.8 \times 5 = 4$
For the interval (5 < n ≤ 15), the histogram shows a frequency density of approximately 0.6 for a width of 10 minutes: $ext{Frequency} = 0.6 \times 10 = 6$
For the interval (15 < n ≤ 25), the density is about 1.2, so: $ext{Frequency} = 1.2 \times 10 = 12$
For the interval (25 < n ≤ 30), the frequency density is around 0.4, thus: $ext{Frequency} = 0.4 \times 5 = 2$
Finally, for the interval (30 < n ≤ 50), the density is about 0.2, yielding: $ext{Frequency} = 0.2 \times 20 = 4$

The completed frequency table is:

Time taken (n minutes)	Frequency
0 < n ≤ 5	4
5 < n ≤ 15	6
15 < n ≤ 25	12
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.

99%

104 rated

Answer

To find the lower quartile (Q1), we need to determine the position of Q1 in the cumulative frequency:

Calculate the total frequency: $ext{Total frequency} = 4 + 6 + 12 + 2 + 4 = 28$
The lower quartile corresponds to the first 25% of the data, which is: $Q1 = \frac{1}{4} \times 28 = 7$
Now, we find where this falls in the cumulative frequency:
- For the interval (0 < n ≤ 5): Cumulative frequency = 4
- For the interval (5 < n ≤ 15): Cumulative frequency = 10
- For the interval (15 < n ≤ 25): Cumulative frequency = 22

Since Q1 = 7 falls in the second interval (5 < n ≤ 15).

Now, we use linear interpolation to estimate the exact value:
- Where the cumulative frequency just before 7 is 4 and just after is 10, we can interpolate: $Q1 = 5 + \left(\frac{7 - 4}{10 - 4}\right) \times (15 - 5)$ $Q1 = 5 + \left(\frac{3}{6}\right) \times 10 = 5 + 5 = 10$

Thus, an estimate for the lower quartile is approximately 10 minutes.

The histogram shows information about the times taken by some students to finish a puzzle - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 2

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

Complete the frequency table for this information.

Find an estimate for the lower quartile of the times taken to finish the puzzle.

Join the GCSE students using SimpleStudy...