IB Mathematics Applications & Interpretation Topic SL 4.10—spearman’s Rank Correlation Coefficient Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 4.10—spearman’s Rank Correlation Coefficient Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 4.10—spearman’s Rank Correlation Coefficient with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.10—spearman’s Rank Correlation Coefficient and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

A city council studies the relationship between the number of public transport trips per month and the monthly expenditure on transport (in dollars) for 9 residents. The data is shown below, with some residents having equal trip counts.

Resident	Trips per Month	Expenditure ($)
A	20	150
B	15	120
C	25	180
D	15	130
E	30	200
F	20	160
G	10	100
H	25	170
I	12	110

Assign ranks to the data, accounting for equal trip counts.

[3]

Calculate Spearman's rank correlation coefficient.

[4]

Explain what your value of Spearman's rank correlation coefficient indicates about the relationship between trips and expenditure.

[4]

The council adjusts the expenditure for resident A from 150 to 145 dollars. Explain whether this affects Spearman's rank correlation coefficient.

[1]

The council plots the original data (not ranks) on a scatter graph and calculates the regression line $y = 5.2 x + 45$ . Estimate the expenditure for 35 trips and explain why this estimate may not be reliable.

[3]

Question 2

SLPaper 1

A university admissions researcher is investigating the relationship between the number of hours per week a student spends on SAT preparation ( $x$ ), and the student's final SAT score ( $y$ ). The table below shows the data for $10$ students.

Study hours per week ( $x$ )	3	5	7	9	11	13	15	18	20	25
SAT score ( $y$ )	1210	1280	1260	1370	1380	1460	1440	1530	1550	1610

Find the Pearson's product-moment correlation coefficient, $r$ , for this data.

[1]

Comment on the strength of the $r$ value found.

[1]

Find the Spearman's rank correlation coefficient, $r_{s}$ , for this data.

[2]

Comment on the strength of the $r_{s}$ value found.

[2]

In the context of this question and the data provided, comment on whether both correlation coefficients should be considered when determining the relationship between study hours and SAT score, or if one should be used in favour of the other.

[2]

Question 3

SLPaper 2

A regional gymnastics competition held in Cardiff used two judges (Judge U and Judge V), each working independently, to score the artistic merit of the final floor routines of $8$ gymnasts on a scale out of $10$ . The gymnasts are labelled $J$ to $Q$ . The scores are shown in the table below.

Gymnast	J	K	L	M	N	O	P	Q
Judge U's score ( $x$ )	6.4	7.8	8.5	9.2	7.1	8.8	6.9	7.5
Judge V's score ( $y$ )	6.8	7.9	8.7	9.1	7.2	8.4	6.5	7.6
Judge U's rank
Judge V's rank

After reviewing the video replay, Judge U decides that gymnast $M$ 's score was too high and decreases the score from $9.2$ to $8.9$ .

Find the Pearson's product-moment correlation coefficient, $r$ , for this data.

[2]

Using the value of $r$ , interpret the relationship between Judge U's scores and Judge V's scores.

[2]

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

[2]

Use your regression equation from the previous part to estimate Judge V's score for a gymnast whose Judge U score was $8.6$ .

[2]

State whether this estimate is reliable. Justify your answer.

[2]

Complete the two empty rank rows in the table above.

[2]

Find the value of the Spearman's rank correlation coefficient, $r_{s}$ .

[2]

Comment on the result obtained for $r_{s}$ .

[2]

Explain why the value of the Spearman's rank correlation coefficient $r_{s}$ does not change.

[1]

Question 4

SLPaper 1

Priya is a sports psychologist for a national athletics team. She is examining the relationship between an athlete's pre-race stress score, on a scale from $1$ to $20$ , and the athlete's performance index in the race, on a scale from $0$ to $100$ .

She selects a sample of $10$ athletes and records the results below.

Athlete	A	B	C	D	E	F	G	H	I	J
Stress score ( $1$ - $20$ )	15	6	18	9	3	13	8	17	11	6
Performance index ( $0$ - $100$ )	52	82	37	69	95	58	76	45	63	88

Priya cannot decide whether to calculate Spearman's rank correlation coefficient, $r_{s}$ , or Pearson's product-moment correlation coefficient, $r_{p}$ .

State one mathematical reason why Priya might choose to calculate $r_{s}$ .

[1]

Complete the table of ranks.

Athlete	A	B	C	D	E	F	G	H	I	J
Stress rank								2		8.5
Performance rank			10

[2]

Calculate $r_{s}$ .

[2]

Comment on why the values of $r_{p}$ and $r_{s}$ are similar.

[1]

Question 5

SLPaper 2

A river monitoring team measured nitrate concentration, in mg/L, for $8$ water samples using a laboratory test and a portable sensor. The results are shown in the table below. In the rank rows, use rank $1$ for the highest concentration.

Sample	$S_1$	$S_2$	$S_3$	$S_4$	$S_5$	$S_6$	$S_7$	$S_8$
Laboratory result ( $x$ )	12.4	15.8	11.1	18.6	14.2	16.9	10.3	13.5
Portable sensor result ( $y$ )	12.9	15.3	11.5	18.8	13.8	16.2	10.8	14.1
Laboratory rank
Portable sensor rank

Find the Pearson's product-moment correlation coefficient, $r$ , for this data.

[2]

Using the value of $r$ , interpret the relationship between the laboratory results and the portable sensor results.

[2]

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

[2]

Use your regression equation from the previous part to estimate the portable sensor result for a water sample with laboratory result $19.4$ mg/L.

[2]

State whether this estimate is reliable. Justify your answer.

[2]

Complete the two empty rank rows in the table above.

[2]

Find the value of the Spearman's rank correlation coefficient, $r_{s}$ .

[2]

Comment on the result obtained for $r_{s}$ .

[2]

After recalibration, the laboratory test revises the result for sample $S_{4}$ from $18.6$ to $18.0$ .

Explain why the value of the Spearman's rank correlation coefficient $r_{s}$ does not change.

[1]

IB Mathematics Applications & Interpretation SL 4.10—spearman’s Rank Correlation Coefficient Questionbank

IB Mathematics Applications & Interpretation SL 4.10—spearman’s Rank Correlation Coefficient Questionbank

Unlock all 36 questions with a free account

IB Mathematics Applications & Interpretation SL 4.10—spearman’s Rank Correlation Coefficient Questionbank

IB Mathematics Applications & Interpretation SL 4.10—spearman’s Rank Correlation Coefficient Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 4.10—spearman’s Rank Correlation Coefficient Questionbank

Unlock all 36 questions with a free account