IB Mathematics Applications & Interpretation Topic SL 4.4—correlation of Data Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 4.4—correlation of Data Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 4.4—correlation of Data with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.4—correlation of Data and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

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 2

SLPaper 1

A statistical study analyzed the correlation between the duration of rainfall in hours ( $r$ ) and the number of umbrellas sold by a shop each day ( $u$ ). The scatter plot below displays the recorded data.

The average duration of rainfall of the recorded days was 4.

The regression line for $u$ on $r$ is given by the equation $u = 6 + 4 r$ .

Calculate the average number of umbrellas sold per day.

[2]

Sketch the regression line on the provided scatter plot.

[2]

Identify the relationship shown by the regression line:

strong positive correlation
strong negative correlation
weak positive correlation
weak negative correlation

[1]

A day has a rainfall duration of $10$ hours. State one reason why the regression equation might be unreliable for predicting the number of umbrellas sold.

[1]

Question 3

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]

Question 4

HLPaper 1

An online language school is trialling a listening-placement quiz for new students. Two equivalent versions were completed by the same students four days apart. Their scores out of 40 are shown.

Student	A	B	C	D	E	F	G
Version P	11	17	20	26	30	34	39
Version Q	12	21	18	30	26	34	29

Identify the specific term used for this method of determining reliability.

[1]

Identify a drawback associated with applying this reliability test.

[1]

Compute the value of Pearson’s product-moment correlation coefficient for the given data.

[2]

Based on your result, justify whether or not the survey effectively demonstrates reliability.

[2]

Question 5

SLPaper 1

A drone engineer records, for six test flights, the distance from the controller, $D$ (in hundreds of metres), and the signal strength, $S$ (as a percentage). The data is shown below.

$D$	1	4	6	7	9	12
$S$	91	74	64	60	51	35

The linear regression model for $S$ on $D$ has equation $S = m D + c$ .

Calculate the values of $m$ and $c$ .

[3]

Identify the value of the Pearson's product-moment correlation coefficient.

[1]

Predict the signal strength on a flight at $800$ m from the controller, based on this regression model.

[2]

IB Mathematics Applications & Interpretation SL 4.4—correlation of Data Questionbank

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IB Mathematics Applications & Interpretation SL 4.4—correlation of Data Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 4.4—correlation of Data Questionbank

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