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18 The table shows the marks obtained by 10 students in spelling tests in January and February - OCR - GCSE Maths - Question 18 - 2021 - Paper 1
Question 18
18 The table shows the marks obtained by 10 students in spelling tests in January and February. Mark in January 26 53 50 48 66 70 44 37 38 50 Mark in February 42 5... show full transcript
Worked Solution & Example Answer:18 The table shows the marks obtained by 10 students in spelling tests in January and February - OCR - GCSE Maths - Question 18 - 2021 - Paper 1
Step 1
Plot the marks for the remaining four students.
Answer
The marks for the remaining students in January and February are as follows:
- Marks for students: January - 44, 37, 38, 50; February - 86, 48, 50.
Ensure to plot the points (44, 86), (37, 48), (38, 50), and (50, 50) on the scatter diagram.
Step 2
Describe the type of correlation shown in the completed scatter diagram.
Answer
The completed scatter diagram demonstrates a positive correlation. As the marks in January increase, the marks in February tend to increase as well, indicating that students who scored higher in January generally scored higher in February.
Step 3
On the scatter diagram, circle the student that made the greatest improvement in their marks from January to February.
Answer
To identify the student with the greatest improvement, look for the point that has the largest vertical distance between January and February on the scatter diagram. This student made an improvement from a lower mark in January to a significantly higher mark in February.
Step 4
Work out the percentage change in this student’s marks from January to February.
Answer
Let the student's January marks be denoted as and February marks as . The formula for percentage change is:
ext{Percentage Change} = rac{F - J}{J} imes 100
Insert the specific values for and to find the percentage change.
Step 5
Is Kai’s method reliable? Give a reason for your answer.
Answer
Kai's method is not reliable because while a line of best fit can estimate a trend, it does not guarantee accuracy for individuals not represented in the data, particularly when absent data may not follow the same pattern established by other students.