Line Graphs and Time Series

Go up from April to the point, then across to the vertical axis.

Look for the point that is nearest the bottom of the graph.

Read the temperature at each of the two times, then find the difference.

Work out what one small square on the vertical axis stands for first.

A month with exactly 6 hours is not more than 6 hours.

Ignore the small ups and downs: compare the start of the graph with the end.

1. The points start at 55 in 2019 and end at 35 in 2024.
2. There is one small rise (2021 to 2022), but overall the line goes down.
3. Answer: the number of members went down over these years.

Read every point first, then work out the change from each month to the next.

Part (a)

1. The sales were March 20, April 35, May 45, June 75, July 85, August 80.
2. The increases are 15, 10, 30 and 10, then a fall of 5.
3. The steepest line, and the greatest increase, is from May to June.

Part (b)

1. 75-45=30
2. Answer: 30 ice creams.

There are 5 small squares between 0 and 1, so work out what one small square stands for.

1. Between 0 and 1 there are 5 small squares, so each small square is 1\div5=0.2 m.
2. The point for week 4 is 4 small squares above 1.
3. 1+4\times0.2=1.8
4. Answer: 1.8 m.

Read the values for Thursday, Friday and Saturday carefully: each small square is 2 parcels.

1. Each small square stands for 2 parcels.
2. Thursday 26, Friday 34, Saturday 40.
3. 26+34+40=100
4. Answer: 100 parcels.

Read the four plotted values and add them, then compare with the total of 16 hours.

Part (a)

1. Each small square is 0.5 hours.
2. Monday 2, Tuesday 3.5, Wednesday 4, Thursday 2.5.
3. 2+3.5+4+2.5=12
4. 16-12=4
5. Answer: 4 hours.

Part (b)

1. Mean = total ÷ number of days.
2. 16\div5=3.2
3. Answer: 3.2 hours.

Find 11:00 halfway between 10:00 and 12:00, go up to the line and across.

Part (a)

1. 11:00 is halfway between 10:00 and 12:00.
2. The temperature was 12°C at 10:00 and 18°C at 12:00.
3. Halfway along the line the temperature is 15°C.
4. Answer: about 15°C.

Part (b)

1. The readings were only taken at 10:00 and 12:00.
2. The straight line between them is a guess at what happened in between, so the reading at 11:00 is only an estimate.

Use the key to tell the two lines apart. Each small square is 2 thousand visitors.

Part (a)

1. In June, 2023 had 18 thousand visitors and 2024 had 16 thousand.
2. In every other month the 2024 line is above the 2023 line.
3. Answer: June.

Part (b)

1. August 2024: 30 thousand. August 2023: 26 thousand.
2. 30-26=4
3. Answer: 4 thousand.

Work out what one small square stands for, read both values, then divide both by their highest common factor.

1. There are 5 small squares between 0 and 20, so each small square is 4 cakes.
2. Saturday: 56 cakes. Monday: 24 cakes.
3. Saturday to Monday is 56:24.
4. Divide both by 8: 7:3.
5. Answer: 7:3.

Look for the pattern that repeats in each year.

Part (a)

1. In 2023 the highest point is Q1 (9). In 2024 the highest point is also Q1 (10).
2. This makes sense: January to March is the coldest part of the year.
3. Answer: Quarter 1.

Part (b)

1. Q4 2024 is 9 hundred units and Q4 2023 is 8 hundred units.
2. The difference is 1 hundred units.
3. Answer: 100 units.

Read all five values, add them, then divide by the number of days.

1. Each small square is 2 emails.
2. Monday 14, Tuesday 22, Wednesday 18, Thursday 26, Friday 20.
3. Total: 14+22+18+26+20=100
4. Mean: 100\div5=20
5. Answer: 20 emails.

Check the gaps between the numbers on the vertical axis, then look at how the points are joined.

Part (a)

1. The labels are 0,\ 10,\ 20,\ 30,\ 50,\ 60, equally spaced.
2. The gap from 30 to 50 is the same distance as the gap from 20 to 30, so the scale is not even (40 is missing).

Part (b)

1. On a time series graph the points are joined in order with straight lines.
2. Ella has drawn a smooth curve through them, which suggests values between the weeks that were never measured.

Look carefully at where the vertical axis starts.

Part (a)

1. Each small square is 2 thousand pounds, and the axis starts at 40.
2. 2020: 42 thousand pounds. 2024: 54 thousand pounds.
3. 54-42=12 thousand pounds.
4. Answer: £12\,000.

Part (b)

1. The 2024 point is 7 small squares above the axis and the 2020 point is 1 small square above it, but the axis starts at 40, not 0.
2. 54\div42 is less than 2, so the profit did not even double.
3. The graph is misleading because the vertical axis does not start at 0.

Work out how much the percentage changes every two years, and continue the pattern.

Part (a)

1. The points are 85,\ 80,\ 75,\ 70,\ 65,\ 60: the percentage goes down by 5 every two years.
2. Continuing the trend: 60-5=55.
3. Answer: about 55%.

Part (b)

1. A prediction just past the last point (2026) can be reasonable.
2. 2040 is 16 years after the last point, and the trend may change in that time (it cannot go on falling by 5 every two years for ever).
3. So the prediction for 2040 is not reliable.

Find the increase, then divide it by the February value and multiply by 100.

1. There are 5 small squares between 0 and 20, so each small square is 4 orders.
2. February: 40 orders. May: 52 orders.
3. Increase: 52-40=12
4. Percentage increase: \frac{12}{40}\times100=30
5. Answer: 30%.

Read both lines for every month. Each small square is 2 phones.

Part (a)

1. Shop A: 30,\ 34,\ 38,\ 36,\ 44,\ 48. Shop B: 26,\ 36,\ 30,\ 28,\ 32,\ 40.
2. Differences: Jan 4, Feb 2, Mar 8, Apr 8, May 12, Jun 8.
3. Answer: May.

Part (b)

1. 44-32=12
2. Answer: 12 phones.

Part (c)

1. Shop A total: 30+34+38+36+44+48=230
2. Shop B total: 26+36+30+28+32+40=192
3. 230-192=38
4. Answer: 38 phones.