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2.5 Data presentation and interpretation

2.5 Data presentation and interpretation

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Question 57

The ambient temperature, T ∘CT\,^\circ\text{C}T∘C, and the cooling time, CCC minutes, required for a specialized industrial freezer to freeze a specific chemical sample were recorded on 6 different operating days. The data is summarized in the table below.

Day123456
TTT202225283031
CCC141621263235
∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930 \sum T = 156, \quad \sum C = 144, \quad \sum T^2 = 4154, \quad \sum C^2 = 3818, \quad \sum TC = 3930 ∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930
a.

Calculate the values of SCCS_{CC}SCC​, STCS_{TC}STC​ and STTS_{TT}STT​ for these data.

[3]
b.

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

[2]
c.

Interpret your value of the PMCC in the context of the relationship between ambient temperature and cooling time.

[1]
d.

On a suitable grid, draw a scatter diagram of cooling time against ambient temperature for these 6 days.

[3]
e.

Determine the equation of the regression line of CCC on TTT in the form C=a+bTC = a + bTC=a+bT.

[3]
f.

Use your regression line to estimate the cooling time required when the ambient temperature is 27 ∘C27\,^\circ\text{C}27∘C.

[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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