Calculate the mean of these five numbers: 3, 7, 4, 8 and 8.
(Total for Question 4 is 2 marks)
5
Three of the numbers in a set are 6, 9 and 5. The mean of the four numbers is 7. Find the fourth number.
(Total for Question 5 is 3 marks)
6
The ages of seven children are: 7, 9, 7, 8, 7, 10, 9.
(a)State the mode.(1)
(b)Find the median age.(2)
(Total for Question 6 is 3 marks)
7
Find the median of these four numbers: 2, 5, 9 and 11.
A) 5
B) 6
C) 7
D) 8
E) 9
(Total for Question 7 is 1 mark)
8
The numbers of books read by six pupils are: 2, 3, 3, 4, 5 and 5. Calculate the mean number of books read, giving your answer to two decimal places.
(Total for Question 8 is 2 marks)
9
Three numbers are 7, 9 and 10. A fourth number x is added so that the mean of the four numbers is 9. Find x.
(Total for Question 9 is 2 marks)
10
Given the list of scores: 13, 17, 17, 14 and 16, find (a) the range and (b) the mode.
(a)Range(1)
(b)Mode(1)
(Total for Question 10 is 2 marks)
11
What is the mean of 2, 4, 6 and 8?
A) 4
B) 5
C) 6
D) 10
E) 20
(Total for Question 11 is 1 mark)
12
Find the mean and the median of these five decimal numbers: 2.5, 3.0, 4.2, 3.8 and 2.5.
(Total for Question 12 is 3 marks)
13
Which list of numbers has no mode?
A) 2, 3, 4
B) 1, 1, 2
C) 3, 4, 3
D) 5, 5, 5
E) 6, 7, 6
(Total for Question 13 is 1 mark)
14
True or false? The mean of a set of numbers must always be between the smallest and largest values. Give a reason for your answer.
(Total for Question 14 is 1 mark)
15
The five numbers are 3, 7, x, 9 and 10. If the median of the five numbers is 8, find x.
(Total for Question 15 is 2 marks)
16
For the list 4, 4, 5, 6, 9, find the mode, the range and the mean.
(Total for Question 16 is 3 marks)
17
Which of these statements is correct? If two different numbers each appear most often in a data set we call the data:
A) Bimodal
B) Unimodal
C) No mode
D) Multisorted
E) Equimodal
(Total for Question 17 is 1 mark)
18
The numbers 4, 6, 8 and 10 have mean 7. The largest number is increased to 14. Find the new mean.
(Total for Question 18 is 2 marks)
19
Class A has 8 pupils with mean score 6. Class B has 6 pupils with mean score 8. Calculate the mean score for all pupils combined, giving your answer to two decimal places.
(Total for Question 19 is 3 marks)
20
The mean of four numbers is 8. Three of the numbers are 3, 8, 7 and the fourth is x. Find x.
(Total for Question 20 is 3 marks)
Mark scheme · EP.M127 Mean, Median, Mode and Range in Depth
Question 1
B1 option B (mean = 6) cao
Answer: B) 6 (mean = (4+6+8)/3 = 18/3 = 6).
Question 2
B1 option B (mode = 5) cao
Answer: B) 5
Question 3
B1 option C (range = 15 - 4 = 11) cao
Answer: C) 11
Question 4
M1 Sum of numbers seen (3+7+4+8+8 = 30) or equivalent method
A1 Mean 30/5 = 6 cao
Answer: 6 (mean = 30/5 = 6).
Question 5
M1 Equation for total 4*7 = 28 or equivalent method seen
M1 Sum of known numbers subtracted: 28 - (6+9+5) = 28 - 20
A1 Fourth number = 8 cao
Answer: 8 (since 4*7 = 28 and 28 - (6+9+5) = 8).
Question 6
(a) B1 Mode = 7 cao
(a) Answer: 7
(b) M1 Correct order or identification of middle position (sort: 7,7,7,8,9,9,10) or note of 4th value
(b) A1 Median = 8 cao
(b) Answer: 8
Question 7
B1 option C (median = (5+9)/2 = 7) cao
Answer: C) 7
Question 8
M1 Total seen: 2+3+3+4+5+5 = 22 or equivalent
A1 Mean = 22/6 = 3.666... => 3.67 to 2 d.p. cao
Answer: 3.67 (mean = 22/6 = 3.666..., rounded to 3.67).
Question 9
M1 Equation for total 4*9 = 36 or equivalent
A1 x = 36 - (7+9+10) = 10 cao
Answer: 10 (since 4*9 = 36 and 36 - 26 = 10).
Question 10
(a) B1 Range = 17 - 13 = 4 cao
(a) Answer: 4
(b) B1 Mode = 17 cao
(b) Answer: 17
Question 11
B1 option B (mean = (2+4+6+8)/4 = 20/4 = 5) cao
Answer: B) 5
Question 12
M1 Correct total or mean method seen (sum = 16.0, mean = 16.0/5)
A1 Mean = 3.2 cao
B1 Median = 3.0 (sorted: 2.5, 2.5, 3.0, 3.8, 4.2) cao
Answer: Mean = 3.2, Median = 3.0
Question 13
B1 option A (all values different so there is no mode) cao
Answer: A) 2, 3, 4
Question 14
B1 Statement true with correct reason (mean is an average of values so weighted between min and max) cao
Answer: True. The mean is an average of the values, so it lies between the smallest and largest number.
Question 15
M1 Middle (3rd) value identified and set equal to 8 (so x must be the middle value)
A1 x = 8 cao
Answer: 8 (x must be the third number when sorted, so x = 8).
Question 16
M1 Method for mean seen (sum 4+4+5+6+9 = 28) or equivalent
A1 Mean = 28/5 = 5.6 cao
B1 Mode = 4 and Range = 9 - 4 = 5 (either may be awarded as independent correct) cao
Answer: Mode = 4, Range = 5, Mean = 5.6
Question 17
B1 option A (bimodal is the correct term) cao
Answer: A) Bimodal
Question 18
M1 Total before and after seen (old total 28, new total 28 + 4 = 32) or equivalent
A1 New mean = 32/4 = 8 cao
Answer: 8 (new mean = 32/4 = 8).
Question 19
M1 Totals for each class found: 8*6 = 48 and 6*8 = 48
M1 Combined total and division seen: (48+48)/(8+6) = 96/14
A1 Combined mean = 96/14 = 6.857142... => 6.86 to 2 d.p. cao
Answer: 6.86 (combined mean = 96/14 approx 6.857142..., rounded to 6.86).
Question 20
M1 Total required for mean seen: 4 * 8 = 32 or equivalent
M1 Subtract sum of known numbers: 32 - (3+8+7) = 32 - 18