17 The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100. (a) Here are the results of another 4 students. French 21 75 48 53 German 30 78 46 61 Plot these results on the scatter diagram. (b) Describe the type and strength of the correlation shown in this diagram. (c) Work out the percentage of the students whose German result was higher than their French result.

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17 The scatter diagram shows the results of 17 students in their French test and their German test - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Question 17

17 The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100. (a) Here are the results of another 4... show full transcript

Worked Solution & Example Answer:17 The scatter diagram shows the results of 17 students in their French test and their German test - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Step 1

Plot these results on the scatter diagram.

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Answer

To plot the results for the additional 4 students on the scatter diagram:

Locate the point for French score 21 and German score 30.
Locate the point for French score 75 and German score 78.
Locate the point for French score 48 and German score 46.
Locate the point for French score 53 and German score 61.

Mark the points accurately and ensure they align correctly on the graph.

Step 2

Describe the type and strength of the correlation shown in this diagram.

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Answer

The correlation shown in the scatter diagram is a strong positive correlation. This indicates that as the scores in the French test increase, the scores in the German test also tend to increase. The points on the scatter plot are closely clustered along an upward slope.

Step 3

Work out the percentage of the students whose German result was higher than their French result.

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Answer

To find the percentage of students whose German test score was higher than their French test score:

Count the total number of students in the dataset (17 original students + 4 additional students = 21 students).
Identify the students whose German scores were higher than their French scores:
- French 21, German 30 (Higher)
- French 75, German 78 (Higher)
- French 48, German 46 (Not Higher)
- French 53, German 61 (Higher)
Count these instances: 3 students have a higher German score.
Calculate the percentage:
$\text{Percentage} = \frac{\text{Number with higher German score}}{\text{Total number of students}} \times 100 = \frac{3}{21} \times 100 \approx 14.29\%$

Thus, approximately 14.29% of the students scored higher in German than in French.

17 The scatter diagram shows the results of 17 students in their French test and their German test - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Worked Solution & Example Answer:17 The scatter diagram shows the results of 17 students in their French test and their German test - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Plot these results on the scatter diagram.

Describe the type and strength of the correlation shown in this diagram.

Work out the percentage of the students whose German result was higher than their French result.

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