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A doctor records the ages, in years, and the heights, in centimetres, of 10 girls - OCR - GCSE Maths - Question 11 - 2019 - Paper 2
Question 11
A doctor records the ages, in years, and the heights, in centimetres, of 10 girls. Age (years) 2 5 3 7 5 8 3 6 9 4 Height (cm) 85 115 93 120 125 90 117 127 103 The... show full transcript
Worked Solution & Example Answer:A doctor records the ages, in years, and the heights, in centimetres, of 10 girls - OCR - GCSE Maths - Question 11 - 2019 - Paper 2
Step 1
Plot the points for the remaining four girls.
Answer
Plot the points for the ages and heights of the remaining four girls, which are as follows:
- Age 3: Height 117 cm
- Age 6: Height 127 cm
- Age 9: Height 103 cm
- Age 4: Height 90 cm
These points should be marked on the scatter diagram accordingly.
Step 2
Step 3
Does the scatter diagram support the doctor’s statement?
Answer
The scatter diagram indicates that a 6-year-old girl, based on the line of best fit, is estimated to be taller than 95 cm. Since the plotted height for a 6-year-old girl is around 127 cm, the scatter diagram does not support the doctor's statement.
Step 4
Explain why the scatter diagram and line of best fit should not be used to estimate the height of a 12-year-old girl.
Answer
The scatter diagram is based on data from a limited sample of girls aged 2 to 9 years old. There is no data for 12-year-olds, which makes any predictions for this age unreliable. Additionally, growth rates can vary significantly after the age of 9, meaning that the extrapolation of data beyond the observed range is likely to be inaccurate.