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Date May 2017 Marks available 2 Reference code 17M.2.SL.TZ1.T_1
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Estimate Question number T_1 Adapted from N/A

Question

The following table shows the average body weight, x , and the average weight of the brain, y , of seven species of mammal. Both measured in kilograms (kg).

M17/5/MATSD/SP2/ENG/TZ1/01

The average body weight of grey wolves is 36 kg.

In fact, the average weight of the brain of grey wolves is 0.120 kg.

Find the range of the average body weights for these seven species of mammal.

[2]
a.

For the data from these seven species calculate r , the Pearson’s product–moment correlation coefficient;

[2]
b.i.

For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.

[2]
b.ii.

Write down the equation of the regression line y on x , in the form y = m x + c .

[2]
c.

Use your regression line to estimate the average weight of the brain of grey wolves.

[2]
d.

Find the percentage error in your estimate in part (d).

[2]
e.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

529 3     (M1)

= 526  (kg)     (A1)(G2)

[2 marks]

a.

0.922   ( 0.921857 )     (G2)

[2 marks]

b.i.

(very) strong, positive     (A1)(ft)(A1)(ft)

 

Note:     Follow through from part (b)(i).

 

[2 marks]

b.ii.

y = 0.000986 x + 0.0923   ( y = 0.000985837 x + 0.0923391 )     (A1)(A1)

 

Note:     Award (A1) for 0.000986 x , (A1) for 0.0923.

Award a maximum of (A1)(A0) if the answer is not an equation in the form y = m x + c .

 

[2 marks]

c.

0.000985837 ( 36 ) + 0.0923391     (M1)

 

Note:     Award (M1) for substituting 36 into their equation.

 

0.128  (kg)  ( 0.127829  (kg) )     (A1)(ft)(G2)

 

Note:     Follow through from part (c). The final (A1) is awarded only if their answer is positive.

 

[2 marks]

d.

| 0.127829 0.120 0.120 | × 100     (M1)

 

Note:     Award (M1) for their correct substitution into percentage error formula.

 

6.52   ( % )   ( 6.52442...   ( % ) )     (A1)(ft)(G2)

 

Note: Follow through from part (d). Do not accept a negative answer.

 

[2 marks]

e.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.
[N/A]
d.
[N/A]
e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
Show 146 related questions
Topic 1—Number and algebra » SL 1.6—Approximating and estimating
Topic 1—Number and algebra
Topic 4—Statistics and probability
Prior learning

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