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Scatter graphs & correlation

10 questions

LessonNot started
A researcher recorded, for each of 1212 secondary schools, the number of computers the school owns and the total number of GCSE passes gained by its pupils last summer. The scatter graph shows the results.20406080100120140160100200300400500600700Number of computersNumber of GCSE passesA local newspaper printed the headline: "Buying more computers raises GCSE results."

Explain why the researcher's data does not support this headline. You must refer to the scatter graph in your answer.
●●●●●Level 43 marksStart
A café recorded, for each of 88 weeks, the amount it spent on local advertising and the number of customers it served that week.

Ben has drawn the straight line shown on the scatter graph and says it is his line of best fit.20406080100120140160100200300400500Spent on advertising (£)Number of customers(a) Give two reasons why Ben's line is not a good line of best fit.

(b) Ben then says: "The correlation between the amount spent on advertising and the number of customers must be weak."

Explain why Ben is wrong.
●●●●●Level 43 marksStart
In an experiment, 99 identical bean plants were each given a different mass of fertiliser. The table shows the mass of fertiliser, in grams, and the height of each plant, in centimetres, after four weeks.
Fertiliser
(g)		Height after 4 weeks (cm)
218
424
627
833
1038
1225
1447
1651
1857
The scatter graph shows the same information.5101520102030405060Fertiliser (g)Height (cm)(a) One of the plants is an outlier. Write down the mass of fertiliser that this plant was given.

(b) Give a possible reason why this plant does not fit the pattern.

(c) Describe the correlation shown by the other eight plants.

(d) Draw a line of best fit for the other eight plants on the scatter graph.
●●●●●Level 45 marksStart

Predicting from a line of best fit

10 questions

LessonNot started
The scatter graph shows the number of hours of exercise per week and the resting pulse rate, in beats per minute, of 14 students. A line of best fit has been drawn.12345678556065707580859095hours of exercise per weekresting pulse (bpm)(a) Use the line of best fit to estimate the resting pulse rate of a student who exercises for 55 hours per week.

(b) Sam says the estimate in part (a) must be reliable, because 55 hours is inside the range of the data. Comment on Sam's statement.
●●●●●Level 44 marksStart
The scatter graph shows the number of hours of sleep and the reaction time, in milliseconds, of 13 people. A line of best fit has been drawn.45678910200210220230240250260270280hours of sleepreaction time (ms)(a) Use the line of best fit to estimate the reaction time of a person who slept for 99 hours.

(b) A person has a reaction time of 250250 milliseconds. Use the line of best fit to estimate the number of hours that person slept.

(c) Explain why your answer to part (b) is only an estimate.
●●●●●Level 44 marksStart
A candle is lit and its length is measured once an hour for the first 66 hours. The results are plotted on a scatter graph and a line of best fit is drawn. The line has equation

L=20−2t,L = 20 - 2t,

where LL cm is the length of the candle and tt is the time in hours since it was lit.

(a) Use the line of best fit to estimate the length of the candle after 4.54.5 hours.

(b) Work out the length that this line of best fit predicts after 1515 hours.

(c) Use your answer to part (b) to explain why the line of best fit should not be used to make a prediction for 1515 hours.
●●●●●Level 45 marksStart