Year 10 - Scatterplots and lines of good fit - Free practice

Year 10 Scatterplots and Lines of Good Fit Worksheets & Practice

Read, draw and interpret scatterplots. Worked solutions every time, free.

Quick answer

How do you construct a scatterplot and draw a line of good fit?

Plot each pair of numerical values as a point on a graph, with one variable on each axis. Describe any association by its direction (positive or negative), form (linear or non-linear) and strength (strong, moderate or weak). Draw a line of good fit by eye so roughly equal numbers of points lie on each side, then use it to make predictions.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 10 scatterplots and lines of good fit: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Describing association from a scatterplot
A scatterplot is drawn using the following eight data points, where $x$ is the number of hours a student studies per week and $y$ is their test score out of 100.

Hours studied ( $x$ ) 2 4 5 6 7 8 9 10
Test score ( $y$ ) 45 52 58 63 68 71 78 82

Describe the association between hours studied and test score in terms of direction, form and strength.
Show worked solution
Key idea: Association is described by direction (positive or negative), form (linear or non-linear) and strength (strong, moderate or weak).
1. Direction: As hours studied increases, test score also increases, so the association is positive.
2. Form: The points rise at a roughly constant rate with no obvious curve, so the form is linear.
3. Strength: The points follow the linear trend closely with little scatter, so the association is strong.
Answer: Strong positive linear association.
Example 2 · Drawing a line of good fit and making a prediction
The table below shows the age of a car (in years) and its advertised selling price (in thousands of dollars) for seven cars.

Age ( $x$ years) 1 2 3 4 5 6 8
Price ( $y$ thousands) 28 24 21 17 14 11 6

A line of good fit is drawn by eye passing through the points $(1, 28)$ and $(8, 6)$ .

(a) Find the equation of this line of good fit. (b) Use your equation to predict the price of a 5-year-old car.
Show worked solution
Key idea: The equation of a straight line is $y = mx + c$ . Use two points on the line to find the gradient, then find the $y$ -intercept.
1. Find the gradient using the two given points:
  $m = \frac{6 - 28}{8 - 1} = \frac{-22}{7} \approx -3.14$
2. Substitute one point, say $(1, 28)$ , into $y = mx + c$ to find $c$ :
  $28 = -3.14 \times 1 + c \implies c \approx 31.14$
3. The equation of the line of good fit is:
  $y = -3.14x + 31.14$
4. Substitute $x = 5$ to predict the price of a 5-year-old car:
  $y = -3.14 \times 5 + 31.14 = -15.70 + 31.14 = 15.44$
Answer: The equation is $y = -3.14x + 31.14$ ; the predicted price of a 5-year-old car is approximately $15 440.
Example 3 · Correlation and causation in context
A researcher collects data from 12 suburbs in Melbourne. She records the average number of ice cream cones sold per day ( $x$ ) and the number of people who visited the local swimming pool that day ( $y$ ). She finds a strong positive linear association between the two variables.

A council member concludes: "Selling more ice cream causes more people to go swimming. We should sell more ice cream to increase pool visits."

(a) Is the council member's conclusion valid? Explain why or why not. (b) Suggest a third variable that could explain the association between ice cream sales and pool visits.
Show worked solution
Key idea: Correlation means two variables are associated, but this does not mean one causes the other. A third variable (a confounding variable) may explain the association.
1. The council member's conclusion is not valid. A strong association (correlation) between two variables does not mean that one variable causes the other.
2. Just because ice cream sales and pool visits rise together does not mean buying ice cream makes people swim.
3. A likely confounding variable is air temperature (or hot weather). On hot days, people are more likely both to buy ice cream and to visit the pool. The temperature is driving both variables.
4. To claim causation, a controlled experiment would be needed, not just observational data.
Answer: The conclusion is not valid. Correlation does not imply causation. Hot weather is a likely confounding variable that causes both ice cream sales and pool visits to increase at the same time.

Hours studied ( $x$ )	2	4	5	6	7	8	9	10
Test score ( $y$ )	45	52	58	63	68	71	78	82

Age ( $x$ years)	1	2	3	4	5	6	8
Price ( $y$ thousands)	28	24	21	17	14	11	6

Common mistakes

Where students usually lose marks

Confusing direction with strength

The points go downward, so the association is weak.

Direction (positive or negative) and strength (strong, moderate or weak) are separate things. A downward trend means a negative association, which can still be strong if the points lie close to the line. Always describe both features separately.

Drawing the line of good fit through the first and last points, not the data

I drew the line through the two end points of the table because those are the most important.

A line of good fit should balance all the data points, with roughly equal numbers of points above and below the line. The first and last values in a table are not necessarily on the line. Choose two points that the balanced line actually passes through.

Using the line to predict far outside the data range

The data goes up to $x = 10$ , so I used the line to predict the value at $x = 50$ .

Predicting within the data range (interpolation) is generally reliable. Predicting far beyond the data range (extrapolation) is unreliable because the trend may not continue. Always note when a prediction is well outside the range of the data.

Claiming causation from a scatterplot

There is a strong positive association, so increasing $x$ causes $y$ to increase.

A scatterplot only shows correlation, not causation. Never say one variable causes another just because they are associated. Always consider whether a third (confounding) variable might explain the relationship.

Try one yourself

Your turn

The table below shows the number of hours studied and the score (out of 100) achieved by 6 students on a test.

Hours studied	1	2	3	4	5	6
Test score	42	51	55	64	72	78

A line of good fit is drawn and its equation is found to be $\text{score} = 7.4 \times \text{hours} + 33$ . Using this equation, what score (out of 100) does the line of good fit predict for a student who studies for 7 hours? Give your answer correct to the nearest whole number.

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About this worksheet

Why we built it

Scatterplots let students see whether two numerical variables are related, and a line of good fit turns that picture into something they can use to make predictions. These Year 10 worksheets step through plotting ordered pairs, describing the association (direction, form and strength), and drawing or using a line of good fit, with full worked solutions on every question so students can check exactly where their reasoning went.

What's covered

Sub-skills your student will practise

✓Plotting two numerical variables as a scatterplot
✓Describing association: direction (positive or negative), form (linear or non-linear) and strength
✓Identifying outliers and commenting on their effect
✓Drawing a line of good fit by eye through the data
✓Using a line of good fit to make predictions within and beyond the data
✓Distinguishing between correlation and causation

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Frequently asked

Questions parents ask about scatterplots and lines of good fit

What does 'line of good fit' mean in Year 10 maths?

A line of good fit (sometimes called a trend line) is a straight line drawn through a scatterplot so that it sits as close as possible to all the data points. In Year 10 students draw this line by eye, balancing the points above and below it roughly equally.

How do students describe the association between two variables in a scatterplot?

Students comment on three things: direction (positive means both variables increase together, negative means one rises as the other falls), form (whether the pattern looks roughly linear or curved), and strength (how tightly the points cluster around the line).

What is the difference between correlation and causation at Year 10 level?

Correlation means two variables tend to move together in the data. Causation means one variable actually causes the change in the other. A scatterplot can show correlation, but students need to reason carefully before concluding that one variable causes another.

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