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2.5 Data presentation and interpretation

2.5 Data presentation and interpretation

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Question 154

A materials engineer is investigating the relationship between the cooling rate, RRR (∘C/min^{\circ}\text{C/min}∘C/min), and the ultimate tensile strength, SSS (MPa\text{MPa}MPa), of a newly developed alloy. Data is collected from 8 different sample batches and is summarised in the table below.

R1020304050607080S582545535502495458435410 \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline R & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \\ \hline S & 582 & 545 & 535 & 502 & 495 & 458 & 435 & 410 \\ \hline \end{array} RS​10582​20545​30535​40502​50495​60458​70435​80410​​

[You may assume that ∑R=360\sum R = 360∑R=360, ∑S=3962\sum S = 3962∑S=3962, ∑R2=20400\sum R^2 = 20400∑R2=20400, ∑RS=168330\sum RS = 168330∑RS=168330 and SSS=23911.5S_{SS} = 23911.5SSS​=23911.5]

a.

Calculate SRSS_{RS}SRS​ and SRRS_{RR}SRR​. Give your answers to 3 significant figures.

[3]
b.

Calculate the product moment correlation coefficient for this data.

[2]
c.

State whether or not your value supports the use of a linear regression equation to predict tensile strength based on cooling rates. Give a reason for your answer.

[2]
d.

Find the equation of the regression line of SSS on RRR giving your answer in the form S=a+bRS = a + bRS=a+bR.

[3]
e.

Interpret the value of bbb.

[1]
f.

Estimate the decrease in tensile strength when moving from a cooling rate of 25 ∘C/min^{\circ}\text{C/min}∘C/min to a cooling rate of 75 ∘C/min^{\circ}\text{C/min}∘C/min.

[2]
Markscheme

2.5 Data presentation and interpretation Questions

  1. A Level
  2. /Maths
  3. /2.5 Data presentation and interpretation

278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.

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