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GCSE · EDEXCEL

2.14D Averages: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Here are the shoe sizes of 10 dancers in a class:
4, 5, 4, 6, 7, 4, 8, 5, 4, 6
Write down the mode of the shoe sizes.

(Total for Question 1 is 1 mark)

Here is a set of data:
3, 7, 3, 9, 7, 2
State whether this data set has one mode, two modes (it is bimodal), or no mode.

(Total for Question 2 is 1 mark)

Here are the ages, in years, of 7 people at a family party:
23, 19, 45, 8, 31, 12, 27
Find the median age.

(Total for Question 3 is 2 marks)

Here is the rainfall, in mm, recorded over 6 days:
0, 3, 12, 0, 7, 15
Work out the range of the rainfall.

(Total for Question 4 is 1 mark)

For each statement, write down whether it is True or False.

(a)If a data set contains a value that is much higher than the rest, the median is usually a better measure of the average than the mean.(1)

(b)The mode of a set of data is always unique.(1)

(c)To find the range of a set of data, you subtract the mean from the largest value.(1)

(Total for Question 5 is 3 marks)

Here are the points scored by a netball team in their last 5 matches:
34, 28, 41, 25, 37
Work out the mean number of points scored.

(Total for Question 6 is 2 marks)

Here are the numbers of minutes 6 students spent on homework one evening:
35, 42, 28, 50, 33, 45
Work out the mean number of minutes. Give your answer correct to 1 decimal place.

(Total for Question 7 is 2 marks)

The mean of five numbers is 9. Four of the numbers are 6, 4, 11 and 14. Work out the fifth number.

(Total for Question 8 is 3 marks)

Two hockey teams recorded the number of goals they scored in their last 6 matches.
Team Red: 2, 1, 3, 0, 4, 2
Team Blue: 1, 2, 2, 3, 1, 3

(a)Work out the mean number of goals for Team Red and the mean number of goals for Team Blue.(2)

(b)Work out the range of goals for Team Red and the range of goals for Team Blue.(2)

(c)Both teams have the same mean. Use the ranges to state which team's goal-scoring was more consistent, giving a reason.(1)

(Total for Question 9 is 5 marks)

The mean temperature over 5 days in February was -2 degrees Celsius. The temperatures on four of the days were -5, 1, -4 and 2 degrees Celsius. Work out the temperature on the fifth day.

(Total for Question 10 is 3 marks)

The mean of the four numbers x, x + 5, x + 7 and 15 is 12. Work out the value of x.

(Total for Question 11 is 3 marks)

8 runners in Group X have a mean finishing time of 42 seconds. 12 runners in Group Y have a mean finishing time of 46 seconds. Work out the mean finishing time for all 20 runners combined.

(Total for Question 12 is 3 marks)

A class of 30 students sat a test. The mean mark was 62. A marking error is then found: one student's mark was recorded as 45 but should have been 75.

(a)Work out the correct mean mark for the class.(3)

(b)Without recalculating, state whether the corrected mean is higher or lower than the original mean, and explain why.(1)

(Total for Question 13 is 4 marks)

The mean of 6 numbers is 15. A seventh number is added to the list, and the mean of all 7 numbers becomes 16. Work out the seventh number.

(Total for Question 14 is 3 marks)

A list of 6 numbers, placed in order, is:
4, 9, x, x + 3, 15, 20
The median of the list is 11. Work out the value of x.

(Total for Question 15 is 3 marks)

The range of five numbers is 17. The greatest of the five numbers is 3g. The least of the five numbers is g - 1. Work out the value of g.

(Total for Question 16 is 3 marks)

A delivery company is deciding which of two drivers, Driver A or Driver B, to keep on for weekend shifts, based on their delivery times, in minutes, over their last 6 shifts.
Driver A: 18, 20, 19, 45, 21, 19
Driver B: 24, 23, 25, 22, 26, 24

(a)Calculate the mean delivery time for Driver A and the mean delivery time for Driver B. Give your answers correct to 2 decimal places where necessary.(3)

(b)Work out the range of delivery times for each driver, and use your answers to recommend which driver the company should keep on for weekend shifts. Give a reason.(3)

(Total for Question 17 is 6 marks)

The table shows the number of pets owned by the people in a survey.
Number of pets: 0, 1, 2, 3
Frequency: 4, 8, x, 6
The mean number of pets owned is 1.5. Work out the value of x.

(Total for Question 18 is 3 marks)

A drama club has 12 boys with a mean age of 14 years, and g girls with a mean age of 16 years. The mean age of all the boys and girls together is 15 years. Work out the value of g.

(Total for Question 19 is 4 marks)

Three consecutive integers can be written as n - 1, n and n + 1. Show that the mean of any three consecutive integers is always equal to their median.

(Total for Question 20 is 3 marks)

Five positive integers have a mean of 6, a median of 5, a mode of 4 and a range of 7. Find a set of five numbers that satisfies all four conditions.

(Total for Question 21 is 4 marks)

A sports club has junior and senior members. The mean age of the junior members is 12 years and the mean age of the senior members is 34 years. The mean age of all the members combined is 20 years. There are 18 more junior members than senior members. Work out the total number of members in the club.

(Total for Question 22 is 5 marks)

Mark scheme · 2.14D Averages: Fluency and Exam Drill

Question 1

B1 4 cao
Answer: 4

Question 2

B1 two modes (bimodal): 3 and 7, oe
Answer: Two modes (bimodal): 3 and 7

Question 3

M1 ages correctly ordered: 8, 12, 19, 23, 27, 31, 45
A1 23 cao
Answer: 23

Question 4

B1 15 (mm) cao
Answer: 15 mm

Question 5

(a) B1 True
(a) Answer: True
(b) B1 False
(b) Answer: False
(c) B1 False
(c) Answer: False

Question 6

M1 34 + 28 + 41 + 25 + 37 (= 165) seen
A1 33 cao
Answer: 33

Question 7

M1 35+42+28+50+33+45 (= 233) seen, or 233/6
A1 38.8 (minutes), awrt 1dp
Answer: 38.8 minutes

Question 8

M1 5 x 9 (= 45) found
M1 45 - (6 + 4 + 11 + 14) (oe: 45 - 35)
A1 10 cao
Answer: 10

Question 9

(a) B1 Team Red mean = 2 (from 2+1+3+0+4+2=12, 12/6=2)
(a) B1 Team Blue mean = 2 (from 1+2+2+3+1+3=12, 12/6=2)
(a) Answer: Team Red mean = 2, Team Blue mean = 2
(b) B1 Team Red range = 4 (from 4 - 0)
(b) B1 Team Blue range = 2 (from 3 - 1)
(b) Answer: Team Red range = 4, Team Blue range = 2
(c) B1 Team Blue, because it has the smaller range (2 compared with 4), so its scores vary less/are more consistent
(c) Answer: Team Blue, because its range (2) is smaller than Team Red's range (4)

Question 10

M1 5 x (-2) (= -10) found
M1 -10 - (-5 + 1 - 4 + 2) (oe: -10 - (-6))
A1 -4 (degrees C) cao
Answer: -4 degrees Celsius

Question 11

M1 4 x 12 = x + (x + 5) + (x + 7) + 15 (oe), leading to 3x + 27 = 48
M1 3x = 21 (oe)
A1 x = 7 cao
Answer: x = 7

Question 12

M1 8 x 42 (= 336) and 12 x 46 (= 552) both found
M1 (336 + 552) / 20 (oe)
A1 44.4 (seconds) cao
Answer: 44.4 seconds

Question 13

(a) M1 30 x 62 (= 1860) found
(a) M1 1860 - 45 + 75 (oe: 1860 + 30)
(a) A1 63 cao
(a) Answer: 63
(b) B1 higher, because the corrected mark (75) is greater than the mark it replaced (45), so the total (and therefore the mean) increases
(b) Answer: Higher, because 75 is greater than the 45 it replaced, so the total mark increases

Question 14

M1 6 x 15 (= 90) found
M1 7 x 16 (= 112) found
A1 22 cao, from 112 - 90
Answer: 22

Question 15

M1 identifies that the median of 6 ordered values is the mean of the 3rd and 4th values: (x + (x + 3)) / 2 = 11
M1 2x + 3 = 22 (oe)
A1 x = 9.5 cao
Answer: x = 9.5

Question 16

M1 3g - (g - 1) (oe: = 2g + 1)
M1 2g + 1 = 17, leading to 2g = 16
A1 g = 8 cao
Answer: g = 8

Question 17

(a) M1 18+20+19+45+21+19 (= 142) and 24+23+25+22+26+24 (= 144) both found
(a) A1 Driver A mean = 23.67 (minutes), awrt 2dp
(a) A1 Driver B mean = 24 (minutes) cao
(a) Answer: Driver A mean = 23.67 minutes, Driver B mean = 24 minutes
(b) B1 Driver A range = 27 (from 45 - 18)
(b) B1 Driver B range = 4 (from 26 - 22)
(b) B1 Driver B recommended (ft from correct ranges), because Driver B's much smaller range shows far more consistent delivery times, even though Driver B's mean is only slightly higher than Driver A's
(b) Answer: Driver A range = 27 minutes, Driver B range = 4 minutes; Driver B is recommended for consistency

Question 18

M1 total pets = (0x4) + (1x8) + (2 x x) + (3x6) (= 26 + 2x) set up
M1 (26 + 2x) / (18 + x) = 1.5 (oe), leading to 26 + 2x = 27 + 1.5x, i.e. 0.5x = 1
A1 x = 2 cao
Answer: x = 2

Question 19

M1 12 x 14 (= 168) found (total age of boys)
M1 sets up (168 + 16g) / (12 + g) = 15 (oe)
M1 168 + 16g = 180 + 15g (oe), leading to g = 12
A1 g = 12 cao
Answer: g = 12

Question 20

M1 sum = (n - 1) + n + (n + 1) (= 3n) correctly found
A1 mean = 3n / 3 = n
A1 states that n is the median (middle value) of n - 1, n, n + 1, so the mean equals the median, cso
Answer: Mean = n = median (shown)

Question 21

M1 uses the mean to find the total of the five numbers: 5 x 6 = 30
M1 uses the mode and median conditions correctly, e.g. two values equal to 4 placed as the two lowest numbers, with 5 as the (3rd, middle) value
M1 uses the range condition with the smallest value (4) to fix the largest value (4 + 7 = 11), then finds the remaining value from the total
A1 a fully correct set of five positive integers satisfying all four conditions, e.g. 4, 4, 5, 6, 11 (accept any other valid set)
Answer: 4, 4, 5, 6, 11 (one valid answer; other correct sets may exist)

Question 22

M1 lets the number of seniors be s, so the number of juniors is s + 18
M1 total age = 12(s + 18) + 34s (oe), correctly expanded to 46s + 216
M1 sets up (46s + 216) / (2s + 18) = 20 (oe)
M1 correctly solves to 46s + 216 = 40s + 360, leading to 6s = 144, s = 24
A1 66 (total members) cao, from 2 x 24 + 18
Answer: 66 members

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