For each statement about pictograms, write down whether it is True or False.
(i)One symbol in a pictogram must always represent exactly one item.(1)
(ii)A pictogram needs a key so that the reader knows how many items one whole symbol stands for.(1)
(Total for Question 1 is 2 marks)
2
The pictogram shows the number of books borrowed from a school library on each of four days.
(a)Write down the number of books borrowed on Tuesday.(1)
(b)Write down the day on which the fewest books were borrowed.(1)
(c)Write down the day on which the most books were borrowed.(1)
(d)Work out the total number of books borrowed over the four days shown.(2)
(Total for Question 2 is 5 marks)
3
Four scout groups took part in a tree-planting day. The pictogram shows how many trees each group planted.
(a)The key states that 1 whole symbol represents 4 trees. Write down how many trees a half symbol represents.(1)
(b)Write down the number of trees planted by Group C.(1)
(c)Work out the number of trees planted by Group D.(2)
(d)Write down which group planted the most trees.(1)
(Total for Question 3 is 5 marks)
4
The pictogram shows the number of overseas parcels processed by a post office on each of five weekdays.
(a)Write down the number of parcels processed on Thursday.(1)
(b)Work out the difference between the number of parcels processed on Friday and on Tuesday.(2)
(c)Work out the difference between the busiest day and the quietest day shown on the pictogram.(2)
(Total for Question 4 is 5 marks)
5
Pupils in a Year 8 class were each asked which type of pet they own (each pupil owns exactly one pet). The results are shown in the pictogram.
(a)Which pet type was owned by the fewest pupils?(1)
A) Dogs
B) Cats
C) Fish
D) Rabbits
(b)Work out how many more pupils own a dog than own a rabbit.(2)
(c)Work out the total number of pupils surveyed.(2)
(Total for Question 5 is 5 marks)
6
A school tuck shop sold four flavours of cereal bar during one lunch break. The pictogram shows the number sold.
(a)Work out the total number of bars sold across all four flavours.(2)
(b)Work out the mean number of bars sold per flavour.(2)
(c)Work out the percentage of the total that were chocolate bars. Give your answer to 1 decimal place.(2)
(Total for Question 6 is 6 marks)
7
Amir, Beth, Chen and Dina were asked how many books they read over the summer holiday.
Name
Books read
Amir
18
Beth
9
Chen
15
Dina
6
Choose a suitable key and draw a pictogram, using the same symbol for a book, to show this information. Make sure your key is clearly shown.
(Total for Question 7 is 4 marks)
8
A museum recorded the number of visitors to its dinosaur exhibit each day for one week. The pictogram shows the results for Monday to Friday.
(a)Work out the total number of visitors to the exhibit over the five days shown.(2)
(b)Work out the range of the number of daily visitors shown on the pictogram.(2)
(c)Write down the day on which the exhibit had the most visitors.(1)
(Total for Question 8 is 5 marks)
9
At a school sports day, medals were awarded to four houses. The pictogram shows the total number of medals won by each house.
(a)Write down the number of medals won by Cedar house.(1)
(b)Write down the four houses in order, from the greatest number of medals to the fewest.(1)
(c)Work out how many more medals Dune house won than Amber house.(2)
(d)Work out the total number of medals awarded to all four houses.(2)
(Total for Question 9 is 6 marks)
10
A bakery recorded the number of cakes it sold in January and in February. The pictogram shows the totals for each month.
(a)Work out the total number of cakes sold across the two months.(2)
(b)Work out the percentage increase in cakes sold from January to February. Give your answer to 1 decimal place.(2)
(Total for Question 10 is 4 marks)
11
A student is investigating the question: 'Do students in older year groups travel further to school, on average, than students in younger year groups?' They plan to collect data from Years 7 to 10 and display the average distance travelled (in km) using a pictogram.
(a)PLAN: Write down a suitable hypothesis for this investigation.(1)
(b)COLLECT: State one way the student could make sure the distances collected from each year group are reliable and can be fairly compared.(1)
(c)PROCESS: Work out the total average distance shown across all four year groups.(2)
(d)PROCESS: Work out how much greater the average distance is for Year 10 than for Year 7.(2)
(e)INTERPRET: Using the values shown on the pictogram, comment on whether the data supports the student's hypothesis.(2)
(Total for Question 11 is 8 marks)
12
Four cricket players' scores in one match were recorded.
Player
Runs scored
Zara
27
Yusuf
18
Priya
9
Omar
36
(a)State a suitable key for a pictogram of this data, so that every player's score can be shown using only whole, half, quarter or three-quarter symbols. Give a reason for your choice.(2)
(b)Using a key of 12 runs per symbol, write down the number of symbols needed to show Priya's score of 9 runs.(1)
(c)Explain one disadvantage of choosing a key value that is too large for a small data set like this one.(1)
(Total for Question 12 is 4 marks)
13
A pictogram shows the number of tickets sold for four home football matches.
(a)Write down the number of tickets sold for Game A, Game B and Game C.(3)
(b)The last symbol for Game D is shaded more than half but less than a whole symbol, and it is not divided into a simple half or quarter. Give your best estimate for the number of tickets sold for Game D, stating a range within which the actual number must lie.(2)
(c)Explain why the exact number of tickets sold for Game D cannot be read precisely from this pictogram.(1)
(Total for Question 13 is 6 marks)
14
The Ridgeway Ramblers walking club wants to show the total distance walked by its members each month. Instead of using a key and repeating a fixed-size symbol, a member drew a single circle for each month, making the circle bigger as the distance increased. The diagram is shown below (with the correct distance for each month labelled).
(a)Explain why varying the SIZE of a single symbol, instead of using a fixed-size symbol with a key, is a misleading way to represent this data.(2)
(b)Suggest a more appropriate way to redraw this pictogram.(2)
(c)Give one reason why a pictogram would not be a suitable choice to display continuous data with many decimal values, such as daily rainfall in mm measured to 1 decimal place.(2)
(Total for Question 14 is 6 marks)
15
A pictogram shows the number of sales made by Cafe Rosa in one week, drawn using 4 whole symbols and 1 half symbol, representing a total of 54 sales.
(a)Work out the value of the key, that is, how many sales one whole symbol represents.(2)
(b)A second cafe, using the same key, sold enough to draw 3 whole symbols and 1 quarter symbol on the pictogram. Work out how many sales this represents.(2)
(Total for Question 15 is 4 marks)
Mark scheme · S17 Pictograms
Question 1
(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
Question 2
(a) B1 25 cao
(a) Answer: 25
(b) B1 Wednesday cao
(b) Answer: Wednesday
(c) B1 Tuesday cao
(c) Answer: Tuesday
(d) M1 15 + 25 + 10 + 20, oe (adds all four daily totals)
(d) A1 70 cao
(d) Answer: 70
Question 3
(a) B1 2 cao
(a) Answer: 2
(b) B1 5 cao
(b) Answer: 5
(c) M1 3 x 4 + 3, oe (3 whole symbols plus a three-quarter symbol)
(c) A1 15 cao
(c) Answer: 15
(d) B1 Group D cao
(d) Answer: Group D
Question 4
(a) B1 60 cao
(a) Answer: 60
(b) M1 130 - 70, oe
(b) A1 60 cao
(b) Answer: 60
(c) M1 130 - 60, oe (Friday, the highest, minus Thursday, the lowest)
(c) A1 70 cao
(c) Answer: 70
Question 5
(a) B1 D cao
(a) Answer: D) Rabbits
(b) M1 8 - 2, oe
(b) A1 6 cao
(b) Answer: 6
(c) M1 8 + 7 + 3 + 2, oe
(c) A1 20 cao
(c) Answer: 20
Question 6
(a) M1 24 + 20 + 10 + 32, oe
(a) A1 86 cao
(a) Answer: 86
(b) M1 86 / 4, oe
(b) A1 21.5 cao
(b) Answer: 21.5
(c) M1 (32 / 86) x 100, oe
(c) A1 awrt 37.2%
(c) Answer: 37.2%
Question 7
B1 a suitable key stated, e.g. 1 symbol = 6 books, so that every value can be shown using only whole or half symbols
B1 Amir's row drawn with 3 whole symbols and Dina's row drawn with 1 whole symbol (ft from key)
B1 Beth's row drawn with 1 whole symbol plus a half symbol and Chen's row drawn with 2 whole symbols plus a half symbol (ft from key)
B1 pictogram fully labelled, with the key clearly shown alongside the diagram
(a) B1 students in older year groups travel further to school, on average, than students in younger year groups oe
(a) Answer: Students in older year groups travel further to school, on average, than students in younger year groups.
(b) B1 e.g. ask a similar number of students from each year group (or take a suitable random sample from each), using the same units (km) and the same question each time oe
(b) Answer: Ask a similar number of students from each year group, using the same units (km) and the same question each time, so the averages can be fairly compared.
(c) M1 1.5 + 2 + 2.5 + 4, oe
(c) A1 10 cao
(c) Answer: 10 km
(d) M1 4 - 1.5, oe
(d) A1 2.5 cao
(d) Answer: 2.5 km
(e) B1 yes, the data supports the hypothesis
(e) B1 because the average distance increases at each year group, from 1.5 km in Year 7 up to 4 km in Year 10 oe
(e) Answer: Yes, the data supports the hypothesis, because the average distance travelled increases steadily from 1.5 km in Year 7 up to 4 km in Year 10.
Question 12
(a) B1 a valid key stated, e.g. 1 symbol = 12 runs (or 9, or 18, or any value for which all four scores give a whole, half, quarter or three-quarter symbol) oe
(a) B1 reason given, e.g. so that no score needs an awkward partial symbol that is hard to draw or read oe
(a) Answer: 1 symbol = 12 runs, because this gives Zara 2.25 symbols, Yusuf 1.5 symbols, Priya 0.75 symbols and Omar 3 symbols - every score can be shown using a whole, half or quarter symbol, with no awkward partial symbols.
(b) B1 three-quarter symbol (0.75 of a symbol) cao
(b) Answer: Three-quarter symbol
(c) B1 e.g. if the key is too large, small scores may be shown as only a tiny sliver of a symbol, which is hard to draw accurately and hard for the reader to interpret precisely oe
(c) Answer: If the key value is too large, a small score may need only a very small partial symbol, which is difficult to draw accurately and difficult for the reader to interpret precisely.
Question 13
(a) B1 Game A: 45 cao
(a) B1 Game B: 30 cao
(a) B1 Game C: 60 cao
(a) Answer: Game A: 45, Game B: 30, Game C: 60
(b) M1 a value or range between 45 and 50 tickets, oe
(b) A1 correct reasoning: the shaded part is more than half a symbol (more than 5) but less than a whole symbol (less than 10), so the total is between 40 + 5 = 45 and 40 + 10 = 50
(b) Answer: Between about 45 and 50 tickets (for example, about 47).
(c) B1 the last symbol is not shaded to a simple recognised fraction (such as a half or quarter) of the key, so only an estimate or range can be given, not an exact value oe
(c) Answer: The last symbol is shaded to an amount that is not a simple half or quarter of the key, so it is only possible to estimate a range for the value, not read off an exact number.
Question 14
(a) B1 the reader tends to compare the area (or visual size) of the symbols, not just their labelled values oe
(a) B1 this exaggerates the difference between months: e.g. the July circle looks far more than 3.5 times the size of the April circle, even though 70 miles is only 3.5 times 20 miles oe
(a) Answer: It is misleading because the reader's eye compares the area of the circles rather than reading exact values from a key, so the visual difference between months looks much larger than the true difference between the distances.
(b) B1 use a symbol of the same fixed size throughout oe
(b) B1 choose a suitable key and repeat (whole/half/quarter) copies of that same-size symbol to represent each month's distance oe
(b) Answer: Use the same size of symbol for every month, choose a sensible key (for example 1 symbol = 10 miles), and show each month's distance by repeating that same-size symbol the correct number of times (using half or quarter symbols where needed).
(c) B1 a pictogram can only show simple partial symbols (such as whole, half or quarter symbols) clearly oe
(c) B1 so data with many decimal places would need oddly-shaped, ambiguous partial symbols that are hard to draw and hard to read accurately oe
(c) Answer: A pictogram can only clearly show simple fractions of a symbol (whole, half, quarter). Data with many decimal values would need awkward, non-standard partial symbols that are difficult to draw and difficult for a reader to interpret accurately, so a different chart (such as a bar chart) is more suitable.