Percentiles: Fluency and Exam Drill - Worksheets, Questions and Revision

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F05D Percentiles: Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The 50th percentile of a data set is the same as its median. State whether this is True or False.

(Total for Question 1 is 1 mark)

Write down the percentile that corresponds to the lower quartile, Q1.

(Total for Question 2 is 1 mark)

Write down the percentile that corresponds to the upper quartile, Q3.

(Total for Question 3 is 1 mark)

A value lies at the 80th percentile of a data set. Write down the percentage of the data that lies at or below this value.

(Total for Question 4 is 1 mark)

There are 16 values in an ordered list. Work out the position of the 25th percentile.

(Total for Question 5 is 1 mark)

There are 30 values in an ordered list. Work out the position of the 90th percentile.

(Total for Question 6 is 1 mark)

There are 12 values in an ordered list. Work out the position of the 75th percentile.

(Total for Question 7 is 1 mark)

The heights, in cm, of 10 seedlings, listed in order, are:
12, 15, 17, 18, 20, 21, 23, 25, 27, 30
Find the 20th percentile of the heights.

(Total for Question 8 is 2 marks)

The times, in seconds, taken by 12 runners in a fun run, listed in order, are:
40, 42, 45, 47, 49, 50, 52, 54, 56, 58, 60, 63
Find the 75th percentile of the times.

(Total for Question 9 is 2 marks)

The scores, out of 30, of 9 students in a test, listed in order, are:
10, 12, 14, 16, 18, 20, 22, 25, 28
Find the 40th percentile of the scores.

(Total for Question 10 is 2 marks)

The weights, in kg, of 11 parcels, listed in order, are:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Find the 60th percentile of the weights.

(Total for Question 11 is 2 marks)

The ages of 14 people at a clinic, listed in order, are:
5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 33, 36, 40
Find the 90th percentile of the ages.

(Total for Question 12 is 2 marks)

The prices, in pounds, of 16 items in a shop, listed in order, are:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Find the 10th percentile of the prices.

(Total for Question 13 is 2 marks)

The time, t (minutes), taken by 50 customers to be served at a bank, is shown in the table.

Time (t minutes)	Frequency	Cumulative frequency
0 < t ≤ 5	6	6
5 < t ≤ 10	14	20
10 < t ≤ 15	18	38
15 < t ≤ 20	12	50

(a)Work out the position of the 44th percentile within the cumulative frequency total.(2)

(b)Write down the class interval that contains the 44th percentile.(1)

(Total for Question 14 is 3 marks)

The distances, d (km), cycled by 60 cyclists in a sponsored bike ride are shown in the table.

Distance (d km)	Frequency	Cumulative frequency
0 < d ≤ 10	8	8
10 < d ≤ 20	20	28
20 < d ≤ 30	20	48
30 < d ≤ 40	12	60

Use linear interpolation to estimate the 55th percentile of the distances cycled.

(Total for Question 15 is 3 marks)

The waiting times, in minutes, for 8 customers at Shop A and 8 customers at Shop B, listed in order, are:

Shop A: 2.0, 2.4, 2.6, 2.9, 3.1, 3.4, 3.6, 4.0
Shop B: 1.8, 2.1, 2.5, 2.8, 3.0, 3.5, 4.2, 4.6

(a)Find the median (the 50th percentile) waiting time for each shop.(2)

(b)The interquartile range of Shop A's waiting times is 1.0 minutes and Shop B's is 1.4 minutes. State which shop has more consistent waiting times, giving a reason.(1)

(Total for Question 16 is 3 marks)

The completion times, t (minutes), of 80 students in an exam are shown in the table.

Time (t minutes)	Frequency	Cumulative frequency
0 < t ≤ 30	8	8
30 < t ≤ 60	20	28
60 < t ≤ 90	25	53
90 < t ≤ 120	17	70
120 < t ≤ 150	10	80

(a)Show that the 30th percentile of the completion times is 54 minutes.(3)

(b)Using your answer to part (a), state the percentage of students who completed the exam in more than 54 minutes.(1)

(Total for Question 17 is 4 marks)

The waiting times, w (minutes), for 100 patients at a clinic are shown in the table. Some of the cumulative frequencies are missing.

Waiting time (w minutes)	Frequency	Cumulative frequency
0 < w ≤ 10	10	10
10 < w ≤ 20	20	?
20 < w ≤ 30	25	?
30 < w ≤ 40	25	?
40 < w ≤ 50	20	100

(a)Complete the cumulative frequency column of the table.(2)

(b)A patient waited 24 minutes. Using linear interpolation, find the percentage of patients who waited 24 minutes or less.(1)

(Total for Question 18 is 3 marks)

The response times, in seconds, of two vending machines were recorded for 50 transactions each and grouped into a table.

Machine P

Time (t seconds)	Frequency	Cumulative frequency
0 < t ≤ 5	11	11
5 < t ≤ 10	20	31
10 < t ≤ 15	11	42
15 < t ≤ 20	8	50

Machine Q

Time (t seconds)	Frequency	Cumulative frequency
0 < t ≤ 5	6	6
5 < t ≤ 10	14	20
10 < t ≤ 15	20	40
15 < t ≤ 20	10	50

(a)Show that the median response time for Machine P is 8.5 seconds.(2)

(b)Use linear interpolation to estimate the median response time for Machine Q.(2)

(c)Machine P's interquartile range is 6 seconds and Machine Q's is 4.5 seconds. Using your medians and these interquartile ranges, state which machine is typically faster and which is more consistent.(1)

(Total for Question 19 is 5 marks)

Mark scheme · F05D Percentiles: Fluency and Exam Drill

Question 1

B1 True cao
Answer: True

Question 2

B1 25th (percentile) cao
Answer: 25th percentile

Question 3

B1 75th (percentile) cao
Answer: 75th percentile

Question 4

B1 80% cao
Answer: 80%

Question 5

B1 4 cao
Answer: 4

Question 6

B1 27 cao
Answer: 27

Question 7

B1 9 cao
Answer: 9

Question 8

M1 position = 0.2 x 10 = 2 (a whole number, so average the 2nd and 3rd values)
A1 16 cao
Answer: 16 cm

Question 9

M1 position = 0.75 x 12 = 9 (a whole number, so average the 9th and 10th values)
A1 57 cao
Answer: 57 seconds

Question 10

M1 position = 0.4 x 9 = 3.6, round up to 4
A1 16 cao
Answer: 16

Question 11

M1 position = 0.6 x 11 = 6.6, round up to 7
A1 8 cao
Answer: 8 kg

Question 12

M1 position = 0.9 x 14 = 12.6, round up to 13
A1 36 cao
Answer: 36

Question 13

M1 position = 0.1 x 16 = 1.6, round up to 2
A1 3 cao
Answer: 3 pounds

Question 14

(a) M1 0.44 x 50
(a) A1 22 cao
(a) Answer: 22
(b) B1 10 < t ≤ 15 cao
(b) Answer: 10 < t ≤ 15

Question 15

M1 position = 0.55 x 60 = 33
M1 20 + ((33 - 28) / 20) x 10, oe
A1 22.5 cao
Answer: 22.5 km

Question 16

(a) B1 Shop A median = 3.0 cao
(a) B1 Shop B median = 2.9 cao
(a) Answer: Shop A: 3.0 minutes; Shop B: 2.9 minutes
(b) B1 Shop A, because its interquartile range (1.0 min) is smaller than Shop B's (1.4 min), oe
(b) Answer: Shop A, because its interquartile range (1.0 minutes) is smaller than Shop B's (1.4 minutes).

Question 17

(a) M1 position = 0.3 x 80 = 24
(a) M1 30 + ((24 - 8) / 20) x 30, oe
(a) A1 = 54, as required
(a) Answer: 54 minutes
(b) B1 70% cao
(b) Answer: 70%

Question 18

(a) M1 running totals found (at least 2 of 30, 55, 80 correct)
(a) A1 all three correct: 30, 55, 80
(a) Answer: 30, 55, 80
(b) B1 40% cao
(b) Answer: 40%

Question 19

(a) M1 5 + ((25 - 11) / 20) x 5, oe
(a) A1 = 8.5, as required
(a) Answer: 8.5 seconds
(b) M1 10 + ((25 - 20) / 20) x 5, oe
(b) A1 11.25 cao
(b) Answer: 11.25 seconds
(c) B1 Machine P is faster (lower median, 8.5 < 11.25) and Machine Q is more consistent (smaller interquartile range, 4.5 < 6), both correct for the mark
(c) Answer: Machine P is typically faster (median 8.5 s < 11.25 s) but Machine Q is more consistent (interquartile range 4.5 s < 6 s).

Question 19

5 marks

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Percentiles: Fluency and Exam Drill - Worksheets, Questions and Revision

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F05D Percentiles: Fluency and Exam Drill

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Question 19

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