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Amelia decides to analyse the heights of members of her school rowing club - AQA - A-Level Maths Mechanics - Question 12 - 2019 - Paper 3
Question 12
Amelia decides to analyse the heights of members of her school rowing club. The heights of a random sample of 10 rowers are shown in the table below. Rowers Height... show full transcript
Worked Solution & Example Answer:Amelia decides to analyse the heights of members of her school rowing club - AQA - A-Level Maths Mechanics - Question 12 - 2019 - Paper 3
Step 1
If Ann's height were discarded, state a reason what, if any, difference this would make to the mean and standard deviation.
Answer
If Ann's height were discarded, this would affect both the mean and standard deviation significantly.
Effects on Mean
Removing Ann’s height of 146 cm, we would recalculate the mean using only the remaining heights:
ar{x}_{new} = rac{(162 + 169 + 172 + 156 + 161 + 159 + 157 + 160 + 160)}{9} = 160.0
This means the mean would increase slightly as Ann's height is less than the original mean (160.6).
Effects on Standard Deviation
The standard deviation would also decrease, because Ann's height is further away from the mean compared to most of the other heights. With her removed, the range of the heights would narrow, thus reducing the standard deviation. The exact new standard deviation could be computed, but it would certainly be less than 6.6.