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Scatter graphs & correlation

10 questions

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Twelve members of an athletics club each ran 100100 m and each did a long jump. The scatter graph shows each member's 100100 m time, in seconds, and the length of their long jump, in metres.1212.51313.51414.51515.51633.544.55100 m time (s)Long jump (m)(a) Describe the correlation shown by the scatter graph.

(b) Sam looks at the scatter graph and says: "This proves that a person's sprinting ability affects how far they can long jump."

Explain why the scatter graph does not show this.
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Ten pupils each sat a maths test and a physics test. Both tests were marked out of 100100.

Ellie plotted their marks and then joined the points with a ruler, as shown. She says this is her line of best fit.3040506070809030405060708090Maths markPhysics mark(a) Explain why what Ellie has drawn is not a line of best fit.

(b) Describe the correlation shown by the ten points.
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Diagram 1 shows, for each of 1212 days, the number of hours of daylight and the number of units of electricity used by a school.891011121314350400450500550600650Hours of daylightElectricity used (units)Diagram 2 shows, for each of 1212 Year 11 pupils, the time taken to travel to school and the mark scored in a maths test.5101520253035202530354045505560Travel time (minutes)Maths mark(a) Describe the correlation shown in Diagram 1.

(b) Describe the correlation shown in Diagram 2.

(c) Explain what your answer to part (b) tells you about travel time and maths marks for these pupils.
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Predicting from a line of best fit

10 questions

LessonNot started
Eleven bean plants were measured on various days in the first week after planting. The scatter graph shows the results, with a line of best fit drawn.1234567510152025days since plantingheight (cm)(a) Use the line of best fit to estimate the height of a bean plant 44 days after planting.

(b) Ravi wants to use the same line of best fit to estimate the height of a bean plant 3030 days after planting. Explain why his estimate is unlikely to be reliable.
●●●●●Level 33 marksStart
For each of 15 small shops, the number of hours hh the shop was open on a Saturday and the shop's takings £TT that day were recorded on a scatter graph.

The shops in the sample were open for between 44 and 99 hours, and the line of best fit has equation

T=45h+60.T = 45h + 60.

(a) Use the line of best fit to estimate the takings of a shop that was open for 77 hours.

(b) Explain why the line of best fit should not be used to estimate the takings of a shop that was open for 2424 hours.

(c) Write down what the number 4545 in the equation tells you about these shops.
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A market stall trader recorded, on 13 market days, the number of hours the stall was open and the number of items sold. The scatter graph shows the results, with a line of best fit drawn.123456781020304050hours openitems sold(a) Use the line of best fit to estimate the number of items sold on a day when the stall was open for 66 hours.

(b) Find the gradient of the line of best fit.

(c) Interpret the gradient of the line of best fit in the context of this question.
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