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Estimated Mean from Grouped Data: Fluency and Exam Drill - Worksheets, Questions and Revision

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GCSE · Statistics

S05D Estimated Mean from Grouped Data: Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the midpoint of the class interval 10 < h ≤ 20.
(Total for Question 1 is 1 mark)
2
Write down the midpoint of the class interval 0 < m ≤ 8.
(Total for Question 2 is 1 mark)
3
State whether this is True or False: The midpoint of a class interval is found by adding the lower and upper boundaries of the interval and dividing by 2.
(Total for Question 3 is 1 mark)
4
State whether this is True or False: An estimated mean calculated from grouped data is always exactly equal to the true mean of the original raw data.
(Total for Question 4 is 1 mark)
5
The length of 20 phone calls made from a shop, in minutes, is grouped below.
Class interval (minutes)Frequency
0 < t ≤ 45
4 < t ≤ 89
8 < t ≤ 126

Write down (i) the modal class, and (ii) the width of each class interval.
(Total for Question 5 is 2 marks)
6
The mass of 20 apples, in grams, is grouped below.
Class interval (g)Frequency
80 < m ≤ 1008
100 < m ≤ 1207
120 < m ≤ 1405

Work out an estimate for the mean mass of an apple.
(Total for Question 6 is 2 marks)
7
The distance cycled by 25 people in one week, in km, is grouped below.
Class interval (km)Frequency
0 < d ≤ 106
10 < d ≤ 2012
20 < d ≤ 307

Work out an estimate for the mean distance cycled.
(Total for Question 7 is 2 marks)
8
The price of 15 second-hand textbooks, in pounds, is grouped below.
Class interval (GBP)Frequency
0 < p ≤ 54
5 < p ≤ 106
10 < p ≤ 155

Work out an estimate for the mean price, giving your answer correct to 2 decimal places.
(Total for Question 8 is 2 marks)
9
The class intervals below are not all the same width.
Class interval (minutes)Frequency
0 < t ≤ 54
5 < t ≤ 1510
15 < t ≤ 406

Write down the midpoints of (i) 5 < t ≤ 15, and (ii) 15 < t ≤ 40.
(Total for Question 9 is 2 marks)
10
For each statement, write down whether it is True or False.
(i) A class interval written 10 < x ≤ 20 includes the value 10, but not the value 20.
(ii) Using narrower class intervals when grouping data always gives an exact mean.
(Total for Question 10 is 2 marks)
11
The waiting time of 30 customers at a pharmacy, in minutes, is grouped below.
Class interval (minutes)Frequency
0 < w ≤ 56
5 < w ≤ 1014
10 < w ≤ 1510

Work out the class interval that contains the median waiting time.
(Total for Question 11 is 2 marks)
12
Write down the class width of the interval 20 < t ≤ 35.
(Total for Question 12 is 1 mark)
13
State whether this is True or False: The modal class is the class interval with the highest frequency.
(Total for Question 13 is 1 mark)
14
The class widths below are not all equal.
Class interval (kg)Frequency
0 < m ≤ 54
5 < m ≤ 1010
10 < m ≤ 206

Using midpoints 2.5, 7.5 and 15, work out an estimate for the mean mass.
(Total for Question 14 is 2 marks)
15
The times, in minutes, that 30 students took to complete a puzzle are grouped below.
Class interval (minutes)Frequency
0 < t ≤ 56
5 < t ≤ 1014
10 < t ≤ 157
15 < t ≤ 203

Calculate an estimate for the mean time taken, giving your answer correct to 1 decimal place.
(Total for Question 15 is 3 marks)
16
The heights, in cm, of 24 tomato plants are grouped below.
Class interval (cm)Frequency
20 < h ≤ 405
40 < h ≤ 6011
60 < h ≤ 808
(a)Calculate an estimate for the mean height of a tomato plant.(2)
(b)Explain why this value is described as an estimate rather than the exact mean height of the 24 plants.(1)
(Total for Question 16 is 3 marks)
17
The mass, in kg, of 40 parcels is grouped below.
Class interval (kg)Frequency
0 < m ≤ 510
5 < m ≤ 1018
10 < m ≤ 158
15 < m ≤ 204
(a)Write down the modal class.(1)
(b)Work out the class interval that contains the median mass.(2)
(Total for Question 17 is 3 marks)
18
The ages, in years, of 50 members of a book club are grouped below. The class widths are not all equal.
Class interval (years)Frequency
10 < a ≤ 208
20 < a ≤ 3016
30 < a ≤ 5018
50 < a ≤ 808
(a)Write down the midpoint of the class interval 30 < a ≤ 50.(1)
(b)Use midpoints 15, 25, 40 and 65 to calculate an estimate for the mean age.(2)
(Total for Question 18 is 3 marks)
19
The table shows the number of hours a group of students spent revising last weekend. The frequency for the class 4 < t ≤ 6 is unknown, shown as y. The estimated mean revision time is 4 hours.
Class interval (hours)FrequencyMidpoint
0 < t ≤ 261
2 < t ≤ 4103
4 < t ≤ 6y5
6 < t ≤ 847

Show that y = 16.
(Total for Question 19 is 3 marks)
20
Two students each grouped the same 15 running times, in minutes, using different class widths, to estimate the mean.

Student A's table
Class interval (min)Frequency
20 < t ≤ 223
22 < t ≤ 246
24 < t ≤ 264
26 < t ≤ 282

Student B's table
Class interval (min)Frequency
20 < t ≤ 249
24 < t ≤ 286

The true mean of the original 15 running times, calculated before grouping, was 23.6 minutes.
(a)Use Student A's table to work out an estimate for the mean running time, correct to 1 decimal place.(1)
(b)Use Student B's table to work out an estimate for the mean running time, correct to 1 decimal place.(1)
(c)The true mean was 23.6 minutes. State which student's estimate is closer to the true mean, and comment on whether using narrower class intervals always gives a more accurate estimate.(1)
(Total for Question 20 is 3 marks)
Mark scheme · S05D Estimated Mean from Grouped Data: Fluency and Exam Drill

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