G10.IGCSE_C16. Scatter Diagram and Correlation

​16. Scatter diagrams and correlation

By Math Department

​IGCSE 0580

A scatter plot (or scatter diagram or scatter graph) explores the relationship between two sets of data. Plotting each pair of numbers as a dot allows you to see whether a general pattern emerges.

Scatter plots are examples of bivariate data sets because they link two variables. Other data sets, such as the heights of people in a group, are univariate because they contain only one variable.

What are scatter plots?

Multiple Choice

Which student scored twice as high on the Science test as they did on the Maths test?

• A

• B

• C

• D

Multiple Choice

Which student scored the highest mark on the Maths test?

• A

• B

• C

• D

Multiple Choice

Luke’s math result was very good but his English result was very poor. Which dot is most likely to represent his results?

• A

• B

• C

• D

Multiple Choice

Areej got a very poor maths result but a very good English result. Which dot is most likely to represent her results?

• A

• B

• C

• D

Multiple Choice

Stefan’s mark for Maths was the same as his mark for English. Which dot is most likely to represent her results?

• A

• B

• C

• D

Drag and Drop

a). Sam conducted a survey and found a strong positive relationship between two sets of data. This is represented in scatter plot ​

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b) Ellen collected two sets of data and found a strong negative relationship between the two sets of data. This is represented in scatter plot ​

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c). Liam plotted two sets of data and found there was no relationship between the two sets of data. This is represented in scatter plot ​​

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d) Ning collected two sets of data and found there was a weak negative relationship between them. This is represented in scatter plot ​

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e) Louis found a weak positive relationship between two sets of data when he plotted them on a scatter plot. This is represented in scatter plot

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Drag these tiles and drop them in the correct blank above

diagram 3

diagram 5

diagram 1

diagram 2

diagram 4

Multiple Choice

What is the type of correlation?

• Negative

• no correlation

• positive

Multiple Choice

What type of correlation does this graph have?

• positive 
• negative
• none
• all of the above

Multiple Choice

What type of correlation does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

If Gold's Gym paid $250 for each TV, how many did they buy?

• 35
• 30
• 45
• 20

Multiple Choice

What phrase best describes the correlation illustrated?

• No correlation

• Strong negative

• Weak positive

• Strong positive

Multiple Choice

Choose all the statements which correctly describe this scatter plot.

• There is a strong positive relation between the two sets of marks.

• Students who did well in history did not do as well in art.

• There is no relationship between the two sets of data.

• Students who did well in history also did well in art.

Lines of best fit

​When points on a scatter plot show a linear correlation, you can use a line to model the data. This line is called the line of best fit or trend line and is drawn through the data so that there are an equal number of points above and below it.

Lines of best fit

Multiple Choice

Which is the best line of best fit?

• Red

• Blue

• Green

• Purple

Multiple Choice

What relationship is suggested by the scatter diagram?

• Line of best fit

• As age increases, weight increases

• As age increases, weight decreases

• No relationship between age and weight

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 140 pages. 

• 12 chapters
• 19 chapters
• 14 chapters
• 21 chapters

Multiple Choice

Using the graph, if someone got a mark of 10 in the general knowledge test, what would you predict their IQ to be?

• 110

• 114

• 111

• 121

Multiple Choice

Use the line of best fit to estimate the chemistry mark for a student who obtained a mark of 90 in mathematics.

• 40

• 60

• 80

• 100

Lines of best fit are used to estimate what might happen between known data values (interpolation) and to predict what might happen beyond known data values (extrapolation).

Interpolation and extrapolation

Multiple Choice

Sam graphed this data on a scatter plot and drew a line of best fit. She used the line to estimate the weight for a height of 2.5 m. Sam was:

• interrogating

• interpolating

• extrapolating

• exonerating

Multiple Choice

Adam graphed this data on a scatter plot and drew a line of best fit. He used the line to estimate the mass for a height of 6.4 m. This is called:

• interrogating

• interpolating

• extrapolating

• exonerating

Multiple Choice

By extrapolation, which of the following height ranges would be the best prediction for a nutrient concentration of 80 mg/L?

• Between 35 and 40 cm

• Between 40 and 45 cm

• Between 45 and 50 cm

• Between 50 and 55 cm

When drawing the line by eye, ensure that there are an equal number of points above and below the line. Also attempt to position the line so the average distance from the line to points above is the same as the average distance to the points below.

Draw the line by eye

Multiple Choice

Which graph shows the best trend line for this data?

The equation of the line

Math Response

Given: y = 10 – 4x

What is the value of x when y = 42?

Type answer here

Correct Answer: -8

Deg^°

Rad

Multiple Choice

The gradient for the trend line in graph A is 4. Select the best estimate below for the gradient of graph B.

• 8

• -8

• 2

• -2

Multiple Choice

Y = 2.65T – 8.1

The equation above represents the line of best fit for data relating temperature (T in °C) of a hothouse and the yield of seedlings (Y in kg) over a certain range of temperature settings.

Select the TRUE statement.

• As the temperature goes up, the yield goes up.

• As the temperature goes up, the yield goes down.

• As the temperature goes up, the yield stays the same.

• There is no correlation between them.

Multiple Choice

Y = 2.65T – 8.1

The equation above represents the line of best fit for data relating temperature (T in °C) of a hothouse and the yield of seedlings (Y in kg) over a certain range of temperature settings.

Use the equation to estimate the yield for a temperature of 10°C.

• 16.5

• 18.4

• 20.1

• 26.5

Multiple Choice

Complete the equation for the line of best fit, correct to one decimal place.

• $$y=-13.3x+51.6$$

• $$y=-13.3x-51.6$$

• $$y=13.3x-51.6$$

• $$y=13.3x+51.6$$

Multiple Choice

The equation for a line of best fit is: v = –8.3p + 5.6

This line shows that the two variables have:

• a positive correlation

• a negative correlation

• no correlation

Multiple Choice

Use the point (90, 70) to complete the equation for the line of best fit. Enter your answer as a decimal.

Let M be mathematics mark and C be chemistry mark. If C = 0.75M+ P, then the value of P is ....

• 0.5

• 1.5

• 2.5

• 3.5