The table shows the ages and heights of 12 children - OCR - GCSE Maths - Question 21 - 2023 - Paper 2
Question 21
The table shows the ages and heights of 12 children.
Age (years) | Height (m)
-----------------|--------------
2 | 0.84
4 | 1... show full transcript
Worked Solution & Example Answer:The table shows the ages and heights of 12 children - OCR - GCSE Maths - Question 21 - 2023 - Paper 2
Step 1
Plot the points for the remaining four children.
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Answer
The remaining four children correspond to the ages 5, 7, 9, and 14 years with heights 1.62 m, 1.42 m, 1.24 m, and 1.68 m, respectively. Their coordinates on the scatter diagram should be plotted accurately.
Step 2
Describe the type of correlation shown in the completed scatter diagram.
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The completed scatter diagram shows a positive correlation as the height tends to increase with age; the points approximately form an upward trend.
Step 3
One of these children is taller than expected for their age. On the scatter diagram, circle the point representing this child.
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Answer
The point representing the child taller than expected for their age is for the child aged 5 years with a height of 1.62 m. This point can be circled on the scatter diagram.
Step 4
Kai is 8 years old. By drawing a line of best fit, estimate Kai's height.
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Answer
To estimate Kai's height, draw a line of best fit through the plotted points on the scatter diagram. The intersection of this line with the vertical line at age 8 will give an estimated height, which can be approximated to around 1.45 m.
Step 5
Describe an assumption you have made in giving your answer to part (d)(i).
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An assumption made is that the relationship between age and height continues to hold linearly for children aged around 8 years, and the model used for prediction is valid based on the provided data.
Step 6
Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.
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Using this data to estimate the height of a child that is 17 years old may be unreliable because the data primarily covers younger children, and growth patterns can vary significantly after a certain age, potentially resulting in inaccurate predictions beyond the available data range.
