Further Mathematics · Pearson Edexcel 9FM0 · Option FS2 · Topic 3

Correlation

Measuring correlation with the product moment and Spearman's rank coefficients, and testing whether it is significant.

3 sub-topics
Taught in Year 13
50 practice questions
3 animated lessons

Practice questions (50) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

3.1Product moment correlation coefficientY13
3.2Spearman's rank correlationY13
3.3Testing for zero correlationY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 50 questions in this topic, free, no account needed.

Correlation

Not needed for Year 12Easy

Calculating the product moment correlation coefficient · Year 13 · 1 mark

$S_{xx} = 25$ , $S_{yy} = 144$ and $S_{xy} = 30$ . What is the product moment correlation coefficient?
(1)

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$r$ ${}= \dfrac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}$ . $D$ : 0.5

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Correlation

Not needed for Year 12Medium

The product moment correlation coefficient · Year 13 · 4 marks

For a set of bivariate data,

S_{xx}

{}= 310, \ S_{yy}

{}= 95, \ S_{xy}

{}= 77.2

(a)
Calculate the product moment correlation coefficient.
(2)
(b)
Interpret your answer.
(1)
(c)
The data are coded using $u = 2x + 5$ and $v = (y - 10)/3$ . State the value of the product moment correlation coefficient between $u$ and $v$ .
(1)

Check your answers before you look at the solution

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Part (a)2 marks

$r$ ${}= \frac{77.2}{\sqrt{310 \times 95}}$
$r = 0.450$

Part (b)1 mark

Moderate positive linear correlation.

Part (c)1 mark

Linear coding with positive scale factors does not change $r$ . $0.450$

Total4

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Correlation

Not needed for Year 12Hard

Spearman's rank correlation · Year 13 · 6 marks

Two judges rank 7 contestants,

P

V

. Judge

A

P 1

Q 2

R 3

S 4

T 5

U 6

V 7

. Judge

B

P 6

Q 7

R 4

S 3

T 5

U 2

V 1

(a)
Calculate Spearman's rank correlation coefficient.
(3)
(b)
Test, at the 5% level, whether there is positive agreement between the judges.
(3)

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Part (a)3 marks

$\sum d^2 = 104$
$r_s$ ${}= 1$ ${}- \frac{6 \times 104}{7(49 - 1)}$ ${}= -0.857$

Part (b)3 marks

$H_0: \rho = 0, \ H_1: \rho > 0$
$n = 7$ , one-tailed 5%. $\text{cv} = 0.7143$
Do not reject H₀: there is insufficient evidence of positive agreement between the judges.

Total6

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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What the specification says

Try 3 questions

Part (a)2 marks

Part (b)1 mark

Part (c)1 mark

Part (a)3 marks

Part (b)3 marks

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