| 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.
Spearman's rank correlation coefficient.
what your value of Spearman's rank correlation coefficient indicates about the relationship between trips and expenditure.
A university admissions researcher is investigating the relationship between the number of hours per week a student spends on SAT preparation (), and the student's final SAT score (). The table below shows the data for students.
| Study hours per week () | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 18 | 20 | 25 |
|---|---|---|---|---|---|---|---|---|---|---|
| SAT score () | 1210 | 1280 | 1260 | 1370 | 1380 | 1460 | 1440 | 1530 | 1550 | 1610 |
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 gymnasts on a scale out of . The gymnasts are labelled to . The scores are shown in the table below.
After reviewing the video replay, Judge U decides that gymnast 's score was too high and decreases the score from to .
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 to , and the athlete's performance index in the race, on a scale from to .
She selects a sample of athletes and records the results below.
Priya cannot decide whether to calculate Spearman's rank correlation coefficient, , or Pearson's product-moment correlation coefficient, .
A river monitoring team measured nitrate concentration, in mg/L, for water samples using a laboratory test and a portable sensor. The results are shown in the table below. In the rank rows, use rank for the highest concentration.
| Sample | ||||||||
|---|---|---|---|---|---|---|---|---|
| Laboratory result () | 12.4 | 15.8 | 11.1 | 18.6 | 14.2 | 16.9 | 10.3 | 13.5 |
| Portable sensor result () | 12.9 | 15.3 | 11.5 | 18.8 | 13.8 | 16.2 | 10.8 | 14.1 |
| Laboratory rank |
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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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on the strength of the value found.
In the context of this question and the data provided, 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.
| Gymnast | J | K | L | M | N | O | P | Q |
|---|
| Judge U's score () | 6.4 | 7.8 | 8.5 | 9.2 | 7.1 | 8.8 | 6.9 | 7.5 |
| Judge V's score () | 6.8 | 7.9 | 8.7 | 9.1 | 7.2 | 8.4 | 6.5 | 7.6 |
| Judge U's rank | ||||||||
| Judge V's rank |
Use your regression equation from the previous part to Judge V's score for a gymnast whose Judge U score was .
whether this estimate is reliable. your answer.
Complete the two empty rank rows in the table above.
Find the value of the Spearman's rank correlation coefficient, .
on the result obtained for .
why the value of the Spearman's rank correlation coefficient does not change.
| Athlete | A | B | C | D | E | F | G | H | I | J |
|---|
| Stress score (-) | 15 | 6 | 18 | 9 | 3 | 13 | 8 | 17 | 11 | 6 |
| Performance index (-) | 52 | 82 | 37 | 69 | 95 | 58 | 76 | 45 | 63 | 88 |
| Athlete | A | B | C | D | E | F | G | H | I | J |
|---|
| Stress rank | 2 | 8.5 | ||||||||
| Performance rank | 10 |
on why the values of and are similar.
| Portable sensor rank |
Use your regression equation from the previous part to the portable sensor result for a water sample with laboratory result mg/L.
whether this estimate is reliable. your answer.
Complete the two empty rank rows in the table above.
Find the value of the Spearman's rank correlation coefficient, .
on the result obtained for .
