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2.5 Data presentation and interpretation

2.5 Data presentation and interpretation

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Question 112

An industrial ceramicist measures the energy consumption, EEE kWh, required to maintain different operating temperatures, TTT ∘C^{\circ}\text{C}∘C, in a specialized kiln. Data from 6 test runs are recorded in the table below.

Run123456
TTT200250300350400450
EEE4558688295102
∑T=1950,∑E=450,∑T2=677500,∑E2=36166,∑TE=156500 \sum T = 1950, \sum E = 450, \sum T^2 = 677500, \sum E^2 = 36166, \sum TE = 156500 ∑T=1950,∑E=450,∑T2=677500,∑E2=36166,∑TE=156500
a.

Calculate the values of STTS_{TT}STT​, SEES_{EE}SEE​ and STES_{TE}STE​ for these measurements.

[3]
b.

Calculate the product moment correlation coefficient (PMCC) for these data.

[2]
c.

Interpret your result from part (b) in the context of the kiln's operation.

[2]
d.

On a suitable grid, draw a scatter diagram of energy consumption against operating temperature for these 6 runs.

[2]
e.

Determine the equation of the regression line of EEE on TTT in the form E=a+bTE = a + bTE=a+bT.

[3]
f.

Use your regression line to estimate the energy consumption for a run with an operating temperature of 320 ∘C^{\circ}\text{C}∘C.

[1]
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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