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MEI sd stats question

Taken from June 23 MEI paper 2 Q18.
Riley is investigating the daily water consumption, in litres, of his household.
He records the amount used for a random sample of 120 days from the previous twelve-month
period.
The daily water consumption, in litres, is denoted by x.
Summary statistics for Riley’s sample are given below.
Sigma(x) = 31164.7 and Sigma(x^2) = 8101050.91 n =120
Mean I got as 260, but I need Standard deviation as well in order to
make a Normal Distribution calculation in part (d).
There is also a Histogram given in the question.
Is it possible to get the sd from the information given or do I need to make use of the histogram?
SD from the mark scheme is 7.89, but how to get it?

Reply 1

Original post
by xlaser31
Taken from June 23 MEI paper 2 Q18.
Riley is investigating the daily water consumption, in litres, of his household.
He records the amount used for a random sample of 120 days from the previous twelve-month
period.
The daily water consumption, in litres, is denoted by x.
Summary statistics for Riley’s sample are given below.
Sigma(x) = 31164.7 and Sigma(x^2) = 8101050.91 n =120
Mean I got as 260, but I need Standard deviation as well in order to
make a Normal Distribution calculation in part (d).
There is also a Histogram given in the question.
Is it possible to get the sd from the information given or do I need to make use of the histogram?
SD from the mark scheme is 7.89, but how to get it?

Theres a formula for variance which is based on the sum of x^2 - mean^2 (roughly). It should be in your textbook/formula sheet?

Reply 2

you can work out the variance and that using the summary data only.

the MEI formula may be slightly different from other boards.

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