IB · Mathematics: Applications & Interpretation SL & HL · Statistics & probability

Correlation & regression: IB Mathematics: Applications & Interpretation questions with answers

Free Correlation & regression questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

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Correlation & regression practice questions

Question 1Structured · 5 marksA* challenge

Two judges scored six dancers.

Dancer	A	B	C	D	E	F
Judge 1	12	18	26	31	35	42
Judge 2	7	12	17	30	22	25

Table 1.1

(a)

Find Spearman’s rank correlation coefficient.

[3]

(b)

Interpret your answer in context.

[1]

(c)

Explain why Spearman’s coefficient may be more appropriate than Pearson’s here.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.829 ranks for both judges (M1) Σd² = 6 (A1) r_s = 0.829 A1	3
(b)	strong agreement strong agreement between the judges R1	1
(c)	scores are rankings, not linear the relationship need not be linear / the scores are subjective ranks R1	1

Question 2Structured · 4 marks

The table shows the age x (months) of a car and its value y (% of new price).

x	23	38	24	21	12	38	20
y	70	50	68	76	81	55	71

Table 2.1

(a)

Find Pearson’s correlation coefficient r.

[2]

(b)

Describe the correlation and explain whether it implies causation.

[2]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	−0.976 GDC (M1) −0.976 A1	2
(b)	strong negative; not necessarily causal strong negative A1 correlation does not imply causation R1	2

Question 3Structured · 13 marks

The table shows the average temperature x °C and the number of ice creams sold y at a kiosk on 8 days.

x	14	18	20	27	25	30	30	41
y	52	29	30	40	60	68	56	102

Table 3.1

(a)

Find Pearson’s product-moment correlation coefficient, r, and describe the correlation.

[3]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use the regression line to estimate the number of ice creams sold when the temperature is 26 °C, and comment on the reliability of your estimate.

[3]

(d)

Interpret the gradient of the regression line in this context.

[1]

(e)

Find Spearman’s rank correlation coefficient r_s, and explain why it may be a more suitable measure if the relationship is not linear.

[4]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	r = 0.807 GDC (M1) r = 0.807 A1 strong positive linear correlation A1	3
(b)	y = 2.26x − 3.27 GDC (M1) y = 2.26x − 3.27 A1	2
(c)	55.5 2.26 × 26 − 3.27 (M1) 55.5 A1 reliable: interpolation and strong correlation R1	3
(d)	increase per degree about 2.26 more ice creams are sold for each 1 °C increase R1	1
(e)	0.743 ranking the data (M1) r_s = 0.743 A2 Spearman measures a monotonic (not necessarily linear) relationship R1	4

Question 4Structured · 5 marks

Two judges award scores to 6 contestants.

Contestant	A	B	C	D	E	F
Judge 1	70	49	69	55	60	54
Judge 2	75	65	63	65	69	54

Table 4.1

(a)

Find Spearman’s rank correlation coefficient, r_s.

[4]

(b)

Comment on the level of agreement between the judges.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.493 ranking both sets of scores (M1) correct ranks A1 Pearson’s coefficient applied to the ranks (M1) r_s = 0.493 A1	4
(b)	moderate agreement moderate positive agreement R1	1

Question 5Structured · 13 marks

The table shows the average temperature x °C and the number of ice creams sold y at a kiosk on 8 days.

x	14	16	21	24	24	35	39	44
y	47	48	63	69	68	63	76	109

Table 5.1

(a)

Find Pearson’s product-moment correlation coefficient, r, and describe the correlation.

[3]

(b)

Find the equation of the regression line of y on x.

[2]

(c)

Use the regression line to estimate the number of ice creams sold when the temperature is 27 °C, and comment on the reliability of your estimate.

[3]

(d)

Interpret the gradient of the regression line in this context.

[1]

(e)

Find Spearman’s rank correlation coefficient r_s, and explain why it may be a more suitable measure if the relationship is not linear.

[4]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	r = 0.855 GDC (M1) r = 0.855 A1 strong positive linear correlation A1	3
(b)	y = 1.51x + 26.8 GDC (M1) y = 1.51x + 26.8 A1	2
(c)	67.7 1.51 × 27 + 26.8 (M1) 67.7 A1 reliable: interpolation and strong correlation R1	3
(d)	increase per degree about 1.51 more ice creams are sold for each 1 °C increase R1	1
(e)	0.892 ranking the data (M1) r_s = 0.892 A2 Spearman measures a monotonic (not necessarily linear) relationship R1	4

Question 6Structured · 5 marks

Two judges award scores to 7 contestants.

Contestant	A	B	C	D	E	F	G
Judge 1	45	78	59	52	66	62	74
Judge 2	58	81	68	68	74	61	81

Table 6.1

(a)

Find Spearman’s rank correlation coefficient, r_s.

[4]

(b)

Comment on the level of agreement between the judges.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.873 ranking both sets of scores (M1) correct ranks A1 Pearson’s coefficient applied to the ranks (M1) r_s = 0.873 A1	4
(b)	strong agreement strong positive agreement R1	1

More Statistics & probability questions

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in