CAIE A-Level Mathematics A2 6.4.6 Unbiased Estimates Questions

Practise calculating unbiased estimates of population mean and variance from raw lists, totals, or summarised sample data.

[Maximum number: 3]

The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table.

Number of green sweets	0	1	2	3	>3
Number of packets	32	50	97	21	0

Calculate an unbiased estimate for the population mean of the number of green sweets in a packet of Frutos, and show that an unbiased estimate of the population variance is 0.783 correct to 3 significant figures.

$\hat{\mu}=\frac{307}{200}$ or 1.535
Marking guidance:

Accept 3sf if nothing better seen (1.53 or 1.54).

$\Sigma x^{2} f=627, \operatorname{Est}\left(\sigma^{2}\right)=\frac{200}{199}\left(\frac{\prime 627^{\prime}}{200}-{ }^{\prime} 1.535^{\prime 2}\right)$ or $\frac{1}{199}\left({ }^{\prime} 627^{\prime}-\frac{{ }^{\prime} 307^{\prime 2}}{200}\right)$
Use of a correct formula with their values.

=0.783
AG Correctly obtained with no errors seen.

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CAIE A-Level Mathematics A2 6.4.6 Unbiased Estimates Questions question 1