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19 students take two tests - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Question 19
19 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students. The table shows the results for the other 2 student... show full transcript
Worked Solution & Example Answer:19 students take two tests - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Step 1
Plot these results on the scatter diagram.
Answer
To plot the results for the two additional students:
- Locate the point corresponding to Test 1 score of 36 and Test 2 score of 44 on the scatter diagram. Place a marker at the coordinate (36, 44).
- Locate the point for the second student with Test 1 score of 38 and Test 2 score of 41. Place another marker at (38, 41).
This visually represents the results of all 12 students.
Step 2
Describe the type of correlation shown in the scatter diagram.
Answer
The scatter diagram illustrates a positive correlation between Test 1 and Test 2 results. As the scores in Test 1 increase, the scores in Test 2 also tend to increase, suggesting a relationship where higher performance in one test is associated with higher performance in the other.
Step 3
Step 4
Use your line of best fit to estimate a result for this student on Test 2.
Answer
From the line of best fit, locate where a Test 1 score of 40 intersects with the line. This value will estimate the corresponding Test 2 score, indicating the expected performance based on the trend seen from other students.
Step 5
Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.
Answer
To determine this percentage, first count how many students scored lower on Test 1 than on Test 2 out of the 12 students. Let’s assume that X out of 12 students fulfill this criterion. The percentage can be calculated as:
Calculate this to find the final percentage.