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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.
Answer
To plot the results of the new students on the scatter diagram, identify the coordinates corresponding to the French and German scores:
- For French score of 21, German score of 30: plot (21, 30)
- For French score of 75, German score of 78: plot (75, 78)
- For French score of 48, German score of 46: plot (48, 46)
- For French score of 53, German score of 61: plot (53, 61)
Make sure that each point is accurately marked on the diagram.
Step 2
Describe the type and strength of the correlation shown in this diagram.
Answer
The scatter diagram shows a strong, positive correlation between the French and German test scores. As students' scores in the French test increase, their scores in the German test also tend to increase. This indicates that higher performance in one language test is associated with higher performance in the other.
Step 3
Work out the percentage of the students whose German result was higher than their French result.
Answer
From the original 17 students, we need to determine how many had a German score higher than their French score.
Let's consider the 17 students:
- (21, 30): German higher
- (75, 78): German higher
- (48, 46): French higher
- (53, 61): German higher
The students with higher German scores are 3 out of 21 students.
Now, calculate the percentage:
Thus, approximately 14.29% of the students scored higher in German than in French.