Here are the number of goals scored by a school football team in their last 9 matches: 2, 1, 0, 3, 1, 2, 1, 4, 1 Write down the mode of the number of goals scored.
(Total for Question 1 is 1 mark)
2
Here are the times, in minutes, taken by 8 runners to complete a park run: 32, 45, 28, 39, 41, 35, 30, 44 Find the median time.
(Total for Question 2 is 2 marks)
3
Here are the heights, in cm, of 7 sunflowers grown by a gardening club: 112, 98, 130, 105, 121, 99, 115 Work out the range of the heights.
(Total for Question 3 is 1 mark)
4
The table shows the favourite school lunch of 38 pupils. Lunch: Sandwiches, Pasta, Pizza, Salad Frequency: 7, 12, 15, 4 Write down the modal favourite lunch.
(Total for Question 4 is 1 mark)
5
For each statement, write down whether it is True or False.
(a)The range of a data set depends only on the highest and lowest values, not on how many times each value occurs.(1)
(b)It is impossible for the mean of a data set to equal a value that is not one of the data values.(1)
(c)For a data set with an even number of values, the median is the mean of the two middle values when the data is placed in order.(1)
(Total for Question 5 is 3 marks)
6
A cricket player scored the following runs in 5 innings: 24, 51, 33, 18, 39 Work out the mean number of runs scored.
(Total for Question 6 is 2 marks)
7
Here is the pocket money, in pounds, received by 6 students in one week: 5, 8, 12, 6, 10, 15 Work out the mean amount of pocket money. Give your answer correct to 2 decimal places.
(Total for Question 7 is 2 marks)
8
A shoe shop wants to know which shoe size to order the most of for their winter stock. State which average (mean, median or mode) would be most useful for this purpose, and give a reason for your choice.
(Total for Question 8 is 2 marks)
9
A student, Ade, is working out the mean of these five numbers: 8, 12, 5, 19, 6. Here is his working: 8 + 12 + 5 + 19 + 6 = 50 Mean = 50 / 4 = 12.5
(a)Identify the error Ade has made in his working.(1)
(b)Work out the correct mean.(2)
(Total for Question 9 is 3 marks)
10
Two tutor groups, 10R and 10G, each of 10 pupils, recorded how many books each pupil read last month. 10R: Books read: 0, 1, 2, 3, 4 Frequency: 1, 2, 4, 2, 1 10G: Books read: 0, 1, 2, 3, 4 Frequency: 0, 3, 4, 3, 0
(a)Show that the mean number of books read is the same for 10R and 10G.(3)
(b)Work out the range for each tutor group, and use your answers to state which tutor group's reading amounts were more consistent.(3)
(Total for Question 10 is 6 marks)
11
The table shows the number of siblings for each pupil in a class of 25. Number of siblings: 0, 1, 2, 3, 4 Frequency: 6, 10, 5, 3, 1 Work out the mean number of siblings.
(Total for Question 11 is 3 marks)
12
A local estate agent is describing the typical house price on a street. Nine of the ten houses on the street sold for around 200,000 pounds each. The tenth house, much larger than the rest, sold for 950,000 pounds. Explain why the median would give a more useful description of the typical house price on this street than the mean.
(Total for Question 12 is 2 marks)
13
A student, Erin, is finding the range of these temperatures, in degrees Celsius, recorded over a week: 3, -5, 8, -2, 6, -1, 4 Erin writes: 'The range is 8 - (-1) = 9.'
(a)Identify the error in Erin's method.(1)
(b)Work out the correct range.(2)
(Total for Question 13 is 3 marks)
14
A list of 7 numbers, placed in order, is: 3, 8, 11, 2x - 1, 19, 24, 30 The median of the list is 15. Work out the value of x.
(Total for Question 14 is 3 marks)
15
10 students in Class A have a mean test score of 60. 15 students in Class B have a mean score of 70. 25 students in Class C have a mean score of 78. Work out the mean score for all 50 students combined.
(Total for Question 15 is 4 marks)
16
A data set has n values with mean m. A new data set is formed by adding a constant amount k to every value in the original data set. Show that the mean of the new data set is m + k.
(Total for Question 16 is 3 marks)
17
The table shows the distance, in km, travelled to school by 40 pupils. Distance (km): 0 < d ≤ 2, 2 < d ≤ 4, 4 < d ≤ 6, 6 < d ≤ 8, 8 < d ≤ 10 Frequency: 12, 14, 8, 4, 2 Work out an estimate for the mean distance travelled.
(Total for Question 17 is 4 marks)
18
A student, Kwame, wants to find the median of this data set: 14, 3, 27, 9, 21, 6, 18 Kwame writes: 'There are 7 numbers, so the median is the 4th number listed, which is 9.'
(a)Explain the error in Kwame's method.(1)
(b)Find the correct median.(1)
(Total for Question 18 is 2 marks)
19
Four numbers are b, b + 7, 2b - 3, and 24. The mean of the four numbers is 16.
(a)Work out the value of b.(3)
(b)Hence work out the range of the four numbers.(2)
(Total for Question 19 is 5 marks)
20
The mean of n numbers is 18. A new number, 42, is added to the list, and the mean of the n + 1 numbers becomes 20. Work out the value of n.
(Total for Question 20 is 4 marks)
21
Six positive integers have a mean of 7, a median of 6.5, a mode of 5, and a range of 9. Find a set of six numbers that satisfies all four conditions.
(Total for Question 21 is 4 marks)
22
In a class, 3/5 of the students are girls and the rest are boys. The mean score of the girls is 68. The mean score of the whole class is 71. Work out the mean score of the boys.
(Total for Question 22 is 5 marks)
Mark scheme · 2.14DB Averages: Fluency and Exam Drill (Part 2)
B1 correct reason, e.g. the mode shows the shoe size that is bought most often/most frequently, which tells the shop what to stock the most of
Answer: Mode, because it identifies the shoe size bought most often, which the shop needs to stock the most of
Question 9
(a) B1 Ade divided by 4 instead of 5, oe (there are 5 numbers in the list, not 4)
(a) Answer: Ade divided the total by 4 instead of by 5
(b) M1 50 / 5
(b) A1 10 cao
(b) Answer: 10
Question 10
(a) M1 10R total books = (0x1)+(1x2)+(2x4)+(3x2)+(4x1) (= 20) seen
(a) M1 10G total books = (0x0)+(1x3)+(2x4)+(3x3)+(4x0) (= 20) seen
(a) A1 both means = 20/10 = 2.0, hence equal, cso
(a) Answer: Both means = 2.0 (shown to be equal)
(b) B1 10R range = 4 (from 4 - 0)
(b) B1 10G range = 2 (from 3 - 1)
(b) B1 10G (ft from correct ranges), because its smaller range shows the number of books read varied less/was more consistent
(b) Answer: 10R range = 4, 10G range = 2; 10G was more consistent
Question 11
M1 total frequency = 6+10+5+3+1 (= 25) used
M1 (0x6)+(1x10)+(2x5)+(3x3)+(4x1) (= 33) found
A1 1.32 cao
Answer: 1.32
Question 12
B1 states that the 950,000 pound house pulls/inflates the mean well above what most houses actually sold for
B1 states that the median is not affected by the one very high value, so it better represents the typical price on the street
Answer: The median is more useful because the one much higher price would pull the mean up, making it look higher than what most houses actually sold for; the median is not affected by this extreme value
Question 13
(a) B1 Erin has used -1 as the lowest value, but -5 is lower/more negative, so -1 is not the minimum, oe
(a) Answer: Erin used -1 as the lowest temperature, but -5 is lower than -1, so -5 is actually the minimum
M1 identifies that for 7 ordered values the median is the 4th value: 2x - 1 = 15
M1 2x = 16 (oe)
A1 x = 8 cao
Answer: x = 8
Question 15
M1 10 x 60 (= 600) found
M1 15 x 70 (= 1050) and 25 x 78 (= 1950) both found
M1 (600 + 1050 + 1950) / 50 (oe) set up
A1 72 cao
Answer: 72
Question 16
M1 original total = n x m (from the definition of the mean)
M1 new total = nm + nk (each of the n values increases by k, so the total increases by n x k)
A1 new mean = (nm + nk) / n = m + k, cso
Answer: New mean = m + k (shown)
Question 17
M1 correct midpoints used: 1, 3, 5, 7, 9
M1 sum of (midpoint x frequency) = 140 found
M1 divides by total frequency = 40
A1 3.5 (km) cao
Answer: 3.5 km
Question 18
(a) B1 the data must be arranged in order (ascending or descending) before finding the middle value; Kwame took the 4th value as listed, not the 4th value once ordered
(a) Answer: Kwame did not put the numbers in order first; the median must be found from the ordered data, not the order the numbers were listed in
(b) B1 14 cao
(b) Answer: 14
Question 19
(a) M1 b + (b + 7) + (2b - 3) + 24 = 4 x 16 (oe), leading to 4b + 28 = 64
(a) M1 4b = 36 (oe)
(a) A1 b = 9 cao
(a) Answer: b = 9
(b) M1 identifies the four values as 9, 16, 15, 24 (ft from their b) and identifies the highest (24) and lowest (9)