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Scatter Diagrams




 
This lesson can be used for revision for the higher Maths GCSE. The examples are quick and concise with exam style questions, go to GCSE Maths if you need more in-depth explanations.


How to draw and use scatter diagrams?
Four things you can be asked for scatter diagram questions.
1. Describe the relationship between the variables: positive correlation, negative correlation or no correlation.
2. Plot a point.
3. Draw a line of best fit.
4. Estimate a value using your line of best fit.

Example 1: The scatter graph shows information about the height and weight for nine students.
The table shows the weight and height for three more students.
(a) On the scatter graph, plot the information from the table.
(b) What type of correlation does this scatter graph show?
(c) The weight of another student is 80 kg. Estimate the height of this student.

Example 2: The scatter graph shows the maths mark and the art mark for each of 15 students.
(a) What type of correlation does the scatter graph show?
(b) Draw a line of best fit on the scatter graph?
Sarah has not got a maths mark. Her art mark is 23.
(c) Use your line of best fit to estimate a maths mark for Sarah.

Example 3: The scatter graph shows information about the height and the arm length of each of 8 students in Year 11.
(a) What type of correlation does this scatter graph show?
A different student in Year 11 has a height of 148 cm.
(b) Estimate the arm length of this student.

Example 4: The scatter graph shows information about 10 apartments in a city. The graph shows the distance from the city centre and the monthly rent of each apartment. The table shows the distance from the city centre and the monthly rent for two other apartments.
(a) On the scatter graph, plot the information from the table.
(b) Describe the relationship between the distance from the city centre and the monthly rent.
An apartment is 2.8 km from the city centre.
(c) Find an estimate for the monthly rent for this apartment.
Example 5: The scatter graph shows some information about 8 cars. For each car it shows the engine size, in litres, and the distance, in kilometres, the car travels in one litre of petrol.
(a) What type of correlation does this scatter graph show?
A different car of the same type has an engine size of 2.5 litres.
(b) Estimate the distance travelled on one liter of petrol by this car.

Example 6: The scatter graph gives some information about 10 cars, of the same type and make. The graph shows the age(years) and the value of each car. The table shows the age and the value of two other cars of the same type and make.
(a) On the scatter graph, plot the information from the table.
(b) Describe the relationship between the age and the value of the cars.
A car of the same type and make is 2 1/2 years old
(c) Estimate the value of the car.

Example 7: A publisher checks documents for errors. He records the number of documents that are checked each day. He also records the total number of errors in the documents each day. The scatter graph shows this information.
On another day, 90 documents are checked. There is a total of 17 errors.
(a) Show this information on the scatter graph
(b) Describe the correlation between the number of documents checked and the total number of errors.
One day 110 documents are checked.
(c) Estimate the total number of errors in these documents.
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Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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