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Year 7 · Algebra · 35 min

Read relationships in real-world graphs

Use genuine Adelaide climate data to read axes, describe increasing and decreasing values, and explain what a graph can tell you.

01 / LEARN

The idea, step by step

Read the axes and the source

A graph shows a relationship between two variables: quantities or categories that can take different values. Read its title, axis labels, units and source before describing its shape.

Here the horizontal variable is month of the year, numbered January 1 to December 12. The vertical variable is mean maximum temperature, measured in degrees Celsius. Each month is paired with one temperature value.

The Bureau of Meteorology published these figures for Adelaide (Kent Town), station 023090. Its all-years-of-record table lists 44 years of temperature data over 1977–2020. The station closed on 31 July 2020. These are historical climate statistics, not temperatures measured during one recent year.

Mean maximum temperature is the average of daily maximum air temperatures for that calendar month across the years of record. For example, the July value 15.4∘C summarises many July daily maximums. It does not say that every July day reached that temperature.

Bureau of Meteorology: Adelaide (Kent Town), station 023090; all-years mean maximum temperature, 1977–2020. Values transcribed from the official monthly climate statistics table.
Month numberMonthMean maximum temperature (°C)
1January29.6
2February29.5
3March26.5
4April22.8
5May19.0
6June16.1
7July15.4
8August16.6
9September19.1
10October22.2
11November25.3
12December27.4

Describe the relationship from left to right

Read a time graph from left to right. Say which interval you mean and what happens to the vertical variable over that interval. Give values to support your description.

From January to July, the monthly mean maximum temperature decreases from 29.6∘C to 15.4∘C. From July to December, it increases from 15.4∘C to 27.4∘C. July is the lowest plotted point; January is the highest.

An increasing graph does not have to rise by the same amount each step. From July to August the increase is 1.2∘C, while from August to September it is 2.5∘C. The graph rises over both intervals, but the second increase is larger.

The connecting segments help you follow the monthly pattern. Use the table for the published values to one decimal place; a value read between labelled grid lines on a graph may only be an estimate.

Adelaide (Kent Town): historical monthly mean maximum temperature

Mean maximum temperature (°C)

Adelaide (Kent Town): historical monthly mean maximum temperatureMonth of the year (January = 1); Mean maximum temperature (°C). Jan: 29.6; Feb: 29.5; Mar: 26.5; Apr: 22.8; May: 19; Jun: 16.1; Jul: 15.4; Aug: 16.6; Sep: 19.1; Oct: 22.2; Nov: 25.3; Dec: 27.4. Segments connect successive monthly averages.0510152025300123456789101112Jan: (1, 29.6)Feb: (2, 29.5)Mar: (3, 26.5)Apr: (4, 22.8)May: (5, 19)Jun: (6, 16.1)Jul: (7, 15.4)Aug: (8, 16.6)Sep: (9, 19.1)Oct: (10, 22.2)Nov: (11, 25.3)Dec: (12, 27.4)

Month of the year (January = 1)

Bureau of Meteorology, Adelaide (Kent Town), station 023090; all-years mean maximum temperature, 1977–2020 (44 years of available temperature data).

Compare values and keep conclusions within the data

To compare two plotted values, name their months and subtract the smaller value from the larger. January's mean maximum is 29.6−15.4=14.2∘C higher than July's. This compares two historical averages, not two particular days.

Month numbers mark positions in a calendar. They are not temperatures, and an increase in month number does not always correspond to an increase in temperature. Describe the observed relationship rather than trying to force one straight-line rule onto it.

The graph contains one published average for each whole month. A line between two points does not supply an exact daily temperature between those months. It also does not predict the temperature on a future date.

A careful conclusion names the place and statistic: 'At Adelaide (Kent Town), the historical monthly mean maximum is lower in July than in January.' The graph alone cannot establish that every July day is cooler than every January day.

A common trap

The July point is 15.4∘C, so that was the maximum temperature on every day in July.

Instead: The point is a historical average of July daily maximums across many years. Individual July days can have different maximum temperatures. The graph does not provide their exact values.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read a point in context

On the included Adelaide (Kent Town) graph, what does the point for month 9 represent? Use the table to give the published value.

  1. Read the horizontal axis: month 9 is September.
  2. Read the September row of the table: the mean maximum temperature is 19.1∘C.
  3. State the statistic and location, so the value is not mistaken for a particular day's weather.
September's historical mean maximum temperature at Adelaide (Kent Town) is 19.1∘C. The point has coordinates (9,19.1).
Example 2

Describe and calculate a decrease

The table gives March as 26.5∘C and June as 16.1∘C. Describe the change in monthly mean maximum temperature from March to June, including its size.

  1. The later value, 16.1, is smaller than the earlier value, 26.5, so the temperature statistic decreases.
  2. Find the size of the decrease: 26.5−16.1=10.4.
  3. Include degrees Celsius and identify the two months in the conclusion.
The monthly mean maximum temperature decreases by 10.4∘C from March to June.
Example 3

Check a claim against the graph

A student says, 'The values increase by the same amount each month from July to October.' Check the claim using July 15.4∘C, August 16.6∘C, September 19.1∘C and October 22.2∘C.

  1. July to August: 16.6−15.4=1.2∘C.
  2. August to September: 19.1−16.6=2.5∘C.
  3. September to October: 22.2−19.1=3.1∘C.
  4. All three changes are increases, but 1.2, 2.5 and 3.1 are different.
The claim is false. The monthly mean maximum increases from July to October, but the increases are unequal.

Check your understanding

The monthly mean maximum is 16.1∘C in June, 15.4∘C in July and 16.6∘C in August. Which month is the turning point between a decrease and an increase? Explain with the values.

Show answer

July is the turning point.

The value decreases from 16.1 in June to 15.4 in July, then increases to 16.6 in August. July is lower than both neighbouring months.

03 / WORKSHEET

Your turn

8 questions · 20 marks · Work at your own pace.

Read the questions online
  1. Use the included Adelaide (Kent Town) climate graph and table. Name the horizontal variable and the vertical variable, including the vertical unit.
    2 marks
  2. Use the included Adelaide (Kent Town) table to state the month and monthly mean maximum temperature at
    1. (a)month 4 and
    2. (b)month 11.
    2 marks
  3. Use the included Adelaide (Kent Town) graph and table. Identify the highest and lowest monthly mean maximum temperatures and their months. Find the difference between these two values.
    3 marks
  4. Use the included Adelaide (Kent Town) graph and table. Describe the relationship between month and mean maximum temperature
    1. (a)from January to July and
    2. (b)from July to December. Include the first and last values for each interval.
    4 marks
  5. March's mean maximum temperature is 26.5∘C and October's is 22.2∘C. Which month has the higher value, and by how much?
    2 marks
  6. The monthly mean maximum temperatures are July 15.4∘C, August 16.6∘C and September 19.1∘C. Calculate each month-to-month increase. Which of these two intervals has the larger increase?
    3 marks
  7. May's mean maximum temperature is 19.0∘C and September's is 19.1∘C. Their points look almost level on the graph. Are the published values equal? Explain using their difference.
    2 marks
  8. The graph uses historical monthly averages for Adelaide (Kent Town), calculated across 1977–2020. Its July mean maximum is 15.4∘C. A student says, 'This graph proves that the maximum temperature on 15 July 2027 will be exactly 15.4∘C.' Is the claim justified? Explain what the plotted value actually represents.
    2 marks
Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

  1. Use the included Adelaide (Kent Town) climate graph and table. Name the horizontal variable and the vertical variable, including the vertical unit.
    2 marks

    Read the horizontal label and month numbering. Award 1 mark for month of the year.

    Read the vertical label. Award 1 mark for mean maximum temperature with degrees Celsius.

    Horizontal: month of the year, numbered January 1 to December 12. Vertical: mean maximum temperature, in degrees Celsius (∘C).
  2. Use the included Adelaide (Kent Town) table to state the month and monthly mean maximum temperature at
    1. (a)month 4 and
    2. (b)month 11.
    2 marks

    Month 4 is April; its row gives 22.8∘C. Award 1 mark for both.

    Month 11 is November; its row gives 25.3∘C. Award 1 mark for both.

    1. (a)April, 22.8∘C.
    2. (b)November, 25.3∘C.
  3. Use the included Adelaide (Kent Town) graph and table. Identify the highest and lowest monthly mean maximum temperatures and their months. Find the difference between these two values.
    3 marks

    Locate the highest plotted point and confirm January 29.6 in the table. Award 1 mark for the month and value.

    Locate the lowest plotted point and confirm July 15.4 in the table. Award 1 mark for the month and value.

    Calculate 29.6−15.4=14.2∘C. Award 1 mark for the difference with units.

    Highest: January, 29.6∘C. Lowest: July, 15.4∘C. Difference: 14.2∘C.
  4. Use the included Adelaide (Kent Town) graph and table. Describe the relationship between month and mean maximum temperature
    1. (a)from January to July and
    2. (b)from July to December. Include the first and last values for each interval.
    4 marks

    Follow the points from January to July. Award 1 mark for decreasing and 1 mark for the correct first and last values.

    Follow the points from July to December. Award 1 mark for increasing and 1 mark for the correct first and last values.

    1. (a)As the months progress from January to July, the mean maximum temperature decreases from 29.6∘C to 15.4∘C.
    2. (b)From July to December it increases from 15.4∘C to 27.4∘C.
  5. March's mean maximum temperature is 26.5∘C and October's is 22.2∘C. Which month has the higher value, and by how much?
    2 marks

    Compare 26.5 with 22.2: March's value is higher. Award 1 mark.

    Subtract 26.5−22.2=4.3∘C. Award 1 mark for the difference with units.

    March has the higher mean maximum temperature, by 4.3∘C.
  6. The monthly mean maximum temperatures are July 15.4∘C, August 16.6∘C and September 19.1∘C. Calculate each month-to-month increase. Which of these two intervals has the larger increase?
    3 marks

    July to August: 16.6−15.4=1.2∘C. Award 1 mark.

    August to September: 19.1−16.6=2.5∘C. Award 1 mark.

    Compare 2.5 with 1.2 and select August–September. Award 1 mark. An increasing graph need not have equal increases.

    July–August increases by 1.2∘C; August–September increases by 2.5∘C. August–September has the larger increase.
  7. May's mean maximum temperature is 19.0∘C and September's is 19.1∘C. Their points look almost level on the graph. Are the published values equal? Explain using their difference.
    2 marks

    The table gives 19.0 and 19.1, which are not equal. Award 1 mark for rejecting equality and identifying September as higher.

    Calculate 19.1−19.0=0.1∘C. Award 1 mark. The table preserves a small difference that may be hard to see on the graph.

    No. September's value is 0.1∘C higher than May's.
  8. The graph uses historical monthly averages for Adelaide (Kent Town), calculated across 1977–2020. Its July mean maximum is 15.4∘C. A student says, 'This graph proves that the maximum temperature on 15 July 2027 will be exactly 15.4∘C.' Is the claim justified? Explain what the plotted value actually represents.
    2 marks

    Reject the exact-date prediction: monthly historical averages do not give the temperature of a particular future day. Award 1 mark.

    Explain that the plotted value summarises July daily maximum temperatures across many years. Award 1 mark.

    No. 15.4∘C is the historical average of July daily maximum temperatures across the years of record; it is not a forecast for 15 July 2027.
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Curriculum reference & lesson scope

Australian Curriculum · 9.0

AC9M7A04: Describe relationships between variables represented in graphs of functions from authentic data.

Interpret a graph made from Bureau of Meteorology monthly climate statistics: identify variables, read values, describe increasing and decreasing intervals, compare changes, and distinguish historical averages from daily observations or forecasts.

Official curriculum source ↗

Source checked 2026-11-02. Schools may sequence content differently.

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