Sec 1 Mathematics Statistical Data Handling topical questions

A class of 20 pupils recorded their pets in a tally: Dog 6, Cat 5, Fish 4, and one smudged row for Hamster.

1. (a)Find the frequency for Hamster.[1]
2. (b)State the total number of pets recorded.[1]
3. (c)Which pet is the most common?[1]

A library pictogram uses one book symbol = 4 books borrowed. The rows read: Monday 2 symbols, Tuesday 2½ symbols, Wednesday 1 symbol, Thursday 3 symbols, Friday 1½ symbols.

1. (a)How many books were borrowed on Tuesday?[1]
2. (b)How many books were borrowed on Friday?[1]
3. (c)How many books were borrowed in total for the week?[2]

The colours of cars in a car park were recorded: Red 12, Blue 9, Silver 15, White 4.

1. (a)Which colour is the most common, and how many cars have it?[1]
2. (b)How many cars are in the car park altogether?[1]
3. (c)How many fewer white cars than blue cars are there?[1]

A survey of 60 commuters at an MRT station records how they will travel home: bus 24, MRT 21, walk 9, car 6. A pie chart is drawn.

1. (a)Calculate the angle for the bus sector.[1]
2. (b)Calculate the angle for the MRT sector.[1]
3. (c)Check all four angles by adding them.[1]

A market pictogram uses one basket symbol = 8 mangosteens. The Saturday rows read 2½, 3 and 1¼ baskets for three stalls.

1. (a)How many mangosteens does the 2½-basket stall show?[1]
2. (b)How many mangosteens does the 3-basket stall show?[1]
3. (c)How many mangosteens does the 1¼-basket stall show?[1]

The 24 members of a smoothie club vote on one flavour: Banana 12, Strawberry 8, Mango 4. The results are drawn as a pie chart.

1. (a)Calculate the angle for Banana.[1]
2. (b)Calculate the angle for Strawberry.[1]
3. (c)Calculate the angle for Mango.[1]
4. (d)Check that your three angles are correct.[1]

A line graph tracks the water level in a tank: 8 am 900 L, 12 pm 600 L, 4 pm 600 L, 8 pm 750 L.

1. (a)By how many litres did the level fall from 8 am to 12 pm?[1]
2. (b)Between which two times was the level unchanged?[1]
3. (c)By how many litres did the level rise from 4 pm to 8 pm?[1]
4. (d)Find the average rate of fall per hour between 8 am and 12 pm.[1]

The masses of 50 eggs are grouped in classes of 10 g: 50–60 g: 8, 60–70 g: 17, 70–80 g: 15, 80–90 g: 10. The data is shown in a histogram.

1. (a)How many eggs have a mass of at least 70 g?[1]
2. (b)Which class interval holds the most eggs?[1]
3. (c)Explain why the exact mass of the heaviest egg cannot be found from the table.[2]

For each set of data, choose the most suitable representation: a bar graph, a line graph, or a histogram.

1. (a)The favourite canteen dish of each of 200 pupils.[1]
2. (b)The temperature of a drink measured every minute for 20 minutes.[1]
3. (c)The masses of 40 parcels, grouped in classes of 1 kg.[1]
4. (d)Explain why a line graph is a poor choice for part (a).[1]

A line graph shows a taxi fare against distance: 0 km → $3.50 and 5 km → $8.00, with a straight line between (and beyond) them.

1. (a)Find the fare charged per kilometre after boarding.[2]
2. (b)Use the graph to find the fare for 9 km.[1]
3. (c)A passenger paid $14.30. How far did they travel?[1]

The masses of 60 durians are grouped in a histogram: under 1 kg: 12; 1 kg to under 1.5 kg: 18; 1.5 kg to under 2 kg: 20; 2 kg to under 2.5 kg: 10.

1. (a)How many durians have a mass of at least 1 kg?[1]
2. (b)State the modal class.[1]
3. (c)What fraction of the durians weigh less than 1.5 kg? Give your answer in its simplest form.[2]

A shop’s advert shows a bar graph of cartons of juice sold: January 40, February 46. The vertical axis starts at 30, and the caption reads “Sales have exploded!”.

1. (a)Find the actual ratio of February sales to January sales.[1]
2. (b)About how many times taller does the February bar look than the January bar on the advert’s scale?[1]
3. (c)Explain why the graph is misleading.[2]
4. (d)State one change that would make the graph fair.[1]

Two schools each draw a pie chart of how their pupils travel. In both charts the “cycle” sector is exactly 90°. School A has 500 pupils and School B has 1 000 pupils.

1. (a)What fraction of each school cycles?[1]
2. (b)Find the number of cyclists in each school.[2]
3. (c)The two sectors are identical in size. Explain why the number of cyclists is not.[1]
4. (d)How many pupils cycle across the two schools altogether?[1]

A class of 32 pupils recorded daily screen time in hours: 0–1: 6, 1–2: 14, 2–3: 8, 3–4: 4. They plan to display the data in a pie chart after first checking it as a histogram.

1. (a)Confirm that the classes are suitable for a histogram.[1]
2. (b)How many pupils spend at least 2 hours on screens?[1]
3. (c)Calculate the pie-chart angle for the 1–2 hour class.[2]
4. (d)Give one reason why a pictogram would be a poor choice for this data.[1]

Two families draw pie charts of monthly spending. Family A’s chart has a food sector of 120°, and Family A spends $1 800 per month. Family B’s food sector is 90°, and Family B spends $2 400 per month.

1. (a)Find Family A’s monthly food spending.[2]
2. (b)Find Family B’s monthly food spending.[2]
3. (c)Family B’s sector is smaller in angle. Explain why its food bill is not smaller.[1]