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KS3 Maths · Year 7 · Chapter 9: Interpreting data · Lesson 3

Scatter graphs and correlation

Year 7About 60 minutesNo calculator45 marks
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Date
A

Do Now

Quick questions to start.

  1. A1
    Needed today

    A point is squares right of the origin and squares up. Write its coordinates.

    [1 mark]
    Answer
  2. A2
    Needed today

    On an axis, small squares stand for kg. What does one small square stand for?

    [1 mark]
    Answer
  3. A3
    Last lesson

    A pie chart for people has radius cm. What radius shows people to the same scale?

    [1 mark]
    Answer
  4. A4
    From chapter 8

    Write in standard form.

    [1 mark]
    Answer
B

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Describe the correlation in each graph and say what it tells you.

Revision timeTest markGraph PShoe sizeTest markGraph Q
Hint Points going up from left to right: positive. Going down: negative. Spread everywhere: none.
  1. B1

    Describe the correlation in each graph and say what it tells you.

    [3 marks]
    TemperatureHeating billGraph RHeightHouse numberGraph S
Example 2

The graph shows the hours pupils practised and their test scores.

(a) What score did the pupil who practised for hours get?
(b) Which pupil does not fit the pattern?
(c) Describe the correlation.

02468101020304050Hours practisedScore
Hint Each small square on the score axis is marks.
  1. B2

    A kiosk sold bottles of water on days.

    (a) How many were sold at C?
    (b) How many days were warmer than C?
    (c) Describe the correlation and what it means.

    [4 marks]
    1015202530020406080Temperature (°C)Bottles sold
    Answer(a) (b)
Example 3

A town's daily sales of ice creams and its cases of sunburn show positive correlation. Does selling ice creams cause sunburn?

Hint Think of something else that makes both go up at the same time.
  1. B3

    Weekly sales of winter coats and the town's heating bills show positive correlation. Does buying coats make heating bills go up? Explain.

    [2 marks]
C

Practice

Year 7
  1. C1

    Lena drives km at different speeds. What correlation would a scatter graph of speed and time taken show? Give a reason.

    [2 marks]
  2. C2

    Maths and science marks show positive correlation. Science and art marks show no correlation. Can you say what correlation there is between maths and art? Explain.

    [2 marks]
  1. C3

    The graph shows the height and mass of dogs.

    (a) How tall is the dog that does not fit the pattern?
    (b) What fraction of the dogs are taller than cm but lighter than kg?

    [3 marks]
    3040506070010203040Height (cm)Mass (kg)
    Answer(a) cm (b)
  2. C4

    A café sells more soup when the weather is colder. On the axes, sketch a scatter graph to show this.

    [2 marks]
    TemperatureCups of soup sold
D

Exam-style questions

GCSE Foundation
  1. D1

    A gardener grows tomato plants and records three things about each plant.

    (a)

    Plants that get more hours of sun grow more tomatoes. Describe this correlation and give a possible reason for it.

    [2 marks]
    (b)

    Plants with more slugs on them grow fewer tomatoes. Describe this correlation and give a possible reason for it.

    [2 marks]
    (c)

    The height of a plant makes no difference to how many tomatoes it grows. What correlation is this?

    [1 mark]
    Answer
    Total for D1: 5 marks
  1. D2

    A garage sells used cars. The scatter graph shows the age and value of each car.

    0246810481216Age of car (years)Value (£1000s)
    (a)

    Describe the correlation. How old is the car that does not fit the pattern?

    [2 marks]
    Answer ; years
    (b)

    How many of the cars are worth more than ?

    [1 mark]
    Answer
    (c)

    What percentage of the cars are worth less than ?

    [2 marks]
    Answer
    Total for D2: 5 marks
  2. D3

    Ryan says, "Selling more ice creams makes more people go swimming."

    A beach café records how many ice creams it sells and how many people swim each day.

    01002003004005004080120160Ice creams soldSwimmers
    (a)

    Describe the correlation.

    [1 mark]
    Answer
    (b)

    How many people swam on the day ice creams were sold?

    [1 mark]
    Answer
    (c)

    Explain why Ryan is wrong.

    [2 marks]
    Total for D3: 4 marks
  3. D4

    The graphs show the weight of parcels and the cost to post them. Priya says, "The heavier the parcel, the more it costs." Sam says, "Heavier parcels cost less to post." Leo says, "The weight makes no difference to the cost."

    WeightCostGraph AWeightCostGraph BWeightCostGraph C
    (a)

    Match each person to a graph.

    [3 marks]
    AnswerPriya , Sam , Leo
    (b)

    Whose statement is most likely to be true? Give a reason.

    [1 mark]
    Total for D4: 4 marks
E

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    In a town, more people buy electric cars, so fewer buy petrol cars. More charging points are built and some petrol stations close. What correlation would you expect, year by year, between (i) electric and petrol cars sold, (ii) electric cars sold and charging points, (iii) petrol cars sold and charging points, (iv) electric cars sold and petrol stations? Do fewer petrol cars cause more charging points? Explain.

    [5 marks]
    Hint 1 · What to try

    For each pair, ask: as one goes up, does the other go up, go down, or neither?

    Hint 2 · The first line

    (i) As electric cars go up, petrol cars go down. (ii) More electric cars, more charging points.

    Hint 3 · The full method

    (iii) Fewer petrol cars, more charging points. (iv) More electric cars, fewer petrol stations. Both changes in (iii) come from people buying electric cars.

F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can describe the correlation in a scatter graph and say what it means.
I can read values from a scatter graph.
I can find a point that does not fit the pattern.
I can explain why a correlation does not show a cause.

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