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GCSE · Statistics

S33 Population Pyramids

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A population pyramid is a pair of back-to-back bar charts that shows the percentage (or number) of people of each sex in different age groups.

(a)In the population pyramids used in this pack, which axis shows the percentage of the population?(1)

A) The vertical axis
B) The horizontal axis

(b)Which side of a population pyramid conventionally shows the data for males?(1)

A) The left-hand side
B) The right-hand side

(c)What name is given to the vertical line that separates the male bars from the female bars?(1)

(Total for Question 1 is 3 marks)

The population pyramid shows the percentage of the population of the town of Ashcombe in each age group, split by sex.

(a)Write down the percentage of Ashcombe's population that is male and aged 30-44.(1)

(b)Write down the percentage of Ashcombe's population that is female and aged 60-74.(1)

(c)Write down the age group that contains the largest percentage of Ashcombe's population (male and female combined).(1)

(Total for Question 2 is 3 marks)

Use the Ashcombe population pyramid shown in Question 2 to answer this question.

(a)Write down the age group in which the percentage of females is greatest.(1)

(b)Write down the age group in which the percentage of males is greatest.(1)

(c)Work out the difference between the percentage of males and the percentage of females aged 75+.(2)

(Total for Question 3 is 4 marks)

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

(i)A population pyramid always has an equal percentage of males and females in every single age group.(1)

(ii)The bars for males and females are usually drawn back-to-back around a shared central (vertical) axis.(1)

(iii)The percentages shown in a population pyramid must add up to 100% across all age groups and both sexes.(1)

(iv)A population pyramid with a wide base and a narrow top always means the country has a large elderly population.(1)

(Total for Question 4 is 4 marks)

Ashcombe has a total population of 8400 people. Use the population pyramid shown in Question 2.

(a)Work out the number of people in Ashcombe aged 0-14.(2)

(b)Work out the number of females in Ashcombe aged 60-74.(2)

(Total for Question 5 is 4 marks)

Use the Ashcombe population pyramid shown in Question 2. Work out the total percentage of Ashcombe's population that is aged under 30 (the 0-14 and 15-29 age groups combined, male and female).

(Total for Question 6 is 2 marks)

Use the shape of the Ashcombe population pyramid shown in Question 2. State whether Ashcombe's population is best described as growing (getting younger) or ageing (getting older), and give a reason based on the shape of the pyramid.

(Total for Question 7 is 2 marks)

The population pyramid shows the percentage of the population of the town of Millport in each age group, split by sex.

(a)Write down the percentage of Millport's population that is female and aged 75+.(1)

(b)Write down the age group that contains the largest percentage of Millport's population (male and female combined).(1)

(Total for Question 8 is 2 marks)

Millport has a total population of 15 000 people. Use the population pyramid shown in Question 8.

(a)Work out the number of people in Millport aged 75+.(2)

(b)Work out the number of males in Millport aged 60-74.(2)

(Total for Question 9 is 4 marks)

Use the Millport population pyramid shown in Question 8.

(a)Work out the total percentage of Millport's population aged 60 or over (the 60-74 and 75+ age groups combined, male and female).(2)

(b)'Elderly' is often defined as aged 65 or over. Explain why your answer to part (a) might overestimate the true percentage of Millport's population aged 65 or over.(1)

(Total for Question 10 is 3 marks)

Compare the population pyramids for Ashcombe (Question 2) and Millport (Question 8).

(a)State one similarity and one difference between the shapes of the two pyramids.(2)

(b)Millport has a much smaller percentage of children (0-14) than Ashcombe. Suggest one possible reason for this.(1)

(c)A newspaper claims: 'Millport's population is younger than Ashcombe's.' Assess whether this claim is correct, using the two pyramids.(2)

(Total for Question 11 is 5 marks)

The table shows the total percentage of the population (male and female combined) in each age group for a village.

Age group	0-14	15-29	30-44	45-59	60-74	75+
Percentage	21%	19%	17%	15%	13%	p%

Work out the value of p.

(Total for Question 12 is 2 marks)

The table shows the percentage of Norbridge's population in each age group, by sex.

Age group	Male %	Female %
0-14	9	8
15-29	10	9
30-44	9	9
45-59	8	9
60-74	7	9
75+	5	8

On the grid provided, draw a population pyramid to show this information.

(Total for Question 13 is 4 marks)

A council wants to construct an up-to-date population pyramid for a ward, to help plan future school places.

(a)Before collecting any data (plan), write down one decision the council should make so the population pyramid can be constructed accurately.(1)

(b)The council decides to collect data using the electoral register (collect). Give one reason why this might not give an accurate population pyramid for the whole ward.(1)

(c)Explain why the council should convert its raw head-count totals into percentages (process) before comparing this year's pyramid with next year's, given that the ward's total population is expected to change.(2)

(d)The new pyramid shows a much larger percentage aged 0-14 than the national average (interpret). Give one implication of this for the council's planning.(1)

(Total for Question 14 is 5 marks)

A student looks at the pyramids for Ashcombe (population 8400, Question 2) and Millport (population 15 000, Question 8), and says: 'Ashcombe has 8% of its population as females aged 60-74, and Millport has 8% of its population as females aged 30-44, so the actual number of people must be the same in both towns.'

(a)Work out the number of females aged 60-74 in Ashcombe.(2)

(b)Work out the number of females aged 30-44 in Millport.(2)

(c)Use your answers to parts (a) and (b) to assess whether the student is correct.(2)

(Total for Question 15 is 6 marks)

In a population pyramid for a village, the 30-44 age group contains 18% of the total population. Within this age group, the ratio of males to females is 5 : 4. Work out the percentage of the village's total population that is male and aged 30-44.

(Total for Question 16 is 3 marks)

Mark scheme · S33 Population Pyramids

Question 1

(a) B1 B cao
(a) Answer: B) The horizontal axis
(b) B1 A cao
(b) Answer: A) The left-hand side
(c) B1 central axis / vertical axis / zero line, oe
(c) Answer: The central (vertical) axis

Question 2

(a) B1 9% cao
(a) Answer: 9%
(b) B1 8% cao
(b) Answer: 8%
(c) B1 0-14 cao
(c) Answer: 0-14

Question 3

(a) B1 15-29 cao
(a) Answer: 15-29
(b) B1 0-14 cao
(b) Answer: 0-14
(c) M1 8 - 5, oe
(c) A1 3 (percentage points) cao
(c) Answer: 3 percentage points

Question 4

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
(iii) B1 True cao
(iii) Answer: True
(iv) B1 False cao
(iv) Answer: False

Question 5

(a) M1 (12+10)/100 x 8400, oe (22% of 8400)
(a) A1 1848 cao
(a) Answer: 1848
(b) M1 8/100 x 8400, oe
(b) A1 672 cao
(b) Answer: 672

Question 6

M1 (12+10) + (8+11), oe
A1 41% cao
Answer: 41%

Question 7

B1 growing / getting younger cao
B1 reason: the pyramid has a wide base (0-14 is the largest age group) that narrows towards the top (75+ is the smallest), which is typical of a young, growing population, oe
Answer: Growing (getting younger); the pyramid has a wide base narrowing to a small top (22% aged 0-14 falling to 13% aged 75+).

Question 8

(a) B1 14% cao
(a) Answer: 14%
(b) B1 75+ cao
(b) Answer: 75+

Question 9

(a) M1 (9+14)/100 x 15000, oe (23% of 15000)
(a) A1 3450 cao
(a) Answer: 3450
(b) M1 10/100 x 15000, oe
(b) A1 1500 cao
(b) Answer: 1500

Question 10

(a) M1 (10+12) + (9+14), oe
(a) A1 45% cao
(a) Answer: 45%
(b) B1 the 60-74 band includes people aged 60-64, who are under 65, so some of the 22% counted are not actually elderly, oe
(b) Answer: The 60-74 age band includes 60-64 year olds, who are under 65, so including all of that band overstates the true 65+ percentage.

Question 11

(a) B1 similarity, e.g. in both towns females make up a bigger share of the oldest age group (75+) than males, oe
(a) B1 difference, e.g. Ashcombe's pyramid narrows towards the top (largest group is 0-14) while Millport's pyramid widens towards the top (largest group is 75+), oe
(a) Answer: Similarity: in both towns, females outnumber males in the 75+ group. Difference: Ashcombe's largest age group is 0-14 (a young, growing shape) while Millport's largest age group is 75+ (an ageing shape).
(b) B1 any sensible reason, e.g. Millport may have a lower birth rate, or younger families may have moved away from Millport, oe
(b) Answer: e.g. Millport may have a lower birth rate than Ashcombe, or young families may have moved elsewhere for work or housing.
(c) B1 the claim is not correct (False) cao
(c) B1 reason: Millport's largest age group is 75+ (23%) and its 0-14 group is only 10%, whereas Ashcombe's largest age group is 0-14 (22%), so Ashcombe has the younger population, oe
(c) Answer: No, the claim is not correct; Millport's population is older, since its biggest age group is 75+ (23%) and its 0-14 group is small (10%), while Ashcombe's biggest age group is 0-14 (22%).

Question 12

M1 100 - (21+19+17+15+13), oe
A1 p = 15 cao
Answer: p = 15

Question 13

B1 a suitable uniform percentage scale used on both sides of the horizontal axis, starting at 0
B1 all six male bars (left) drawn to the correct length: 9, 10, 9, 8, 7, 5 (± half a small square)
B1 all six female bars (right) drawn to the correct length: 8, 9, 9, 9, 9, 8 (± half a small square)
B1 pyramid fully labelled, with Male and Female headings and all six age groups labelled
Answer: Pyramid with male bars 9, 10, 9, 8, 7, 5 and female bars 8, 9, 9, 9, 9, 8 (age order 0-14 to 75+).

Question 14

(a) B1 any sensible planning decision, e.g. fix the exact age-band boundaries and a single reference date, and make sure every resident is counted exactly once, oe
(a) Answer: e.g. Decide the exact age-band boundaries (such as 0-14, 15-29, ...) and a single reference date, so every resident is counted once in exactly one group.
(b) B1 the electoral register excludes people who are not registered to vote, e.g. everyone under 18 and any unregistered adults, so young age groups would be undercounted, oe
(b) Answer: The electoral register does not include people under 18 (or unregistered adults), so the youngest age groups would be missing or undercounted.
(c) B1 percentages show each age group's share of the population, regardless of the population's overall size, oe
(c) B1 so if the total population grows or shrinks, percentages still allow a fair, like-for-like comparison of the age structure between the two years, oe (raw counts would rise/fall just because the total changed, even if the age structure had not)
(c) Answer: Percentages show each age group's share of the total, so they can be compared fairly even if the ward's overall population size changes; raw counts alone could rise or fall just because the total population changed, not because the age structure did.
(d) B1 any sensible implication, e.g. the ward is likely to need more primary school places (or related child services) than an average ward, oe
(d) Answer: e.g. The council is likely to need to plan for more primary school places (or nurseries/child health services) than a ward with an average age structure.

Question 15

(a) M1 8/100 x 8400, oe
(a) A1 672 cao
(a) Answer: 672
(b) M1 8/100 x 15000, oe
(b) A1 1200 cao
(b) Answer: 1200
(c) B1 the student is not correct (False) cao
(c) B1 reason: 672 people is not equal to 1200 people; the same percentage represents different actual numbers because Ashcombe and Millport have different total populations, oe
(c) Answer: No, the student is not correct: 672 people (Ashcombe) is not equal to 1200 people (Millport); the same percentage gives different actual numbers because the two towns have different total populations.

Question 16

M1 5+4 (=9) parts, oe (splits the 5:4 ratio into 9 equal parts)
M1 18 / 9 x 5, oe (dep on M1)
A1 10% cao
Answer: 10%

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