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Question
The company Fresh Water produces one-litre bottles of mineral water. The company wants to determine the amount of magnesium, in milligrams, in these bottles.
A random sample of ten bottles is analysed and the results are as follows:
6.7, 7.2, 6.7, 6.8, 6.9, 7.0, 6.8, 6.6, 7.1, 7.3.
Find unbiased estimates of the mean and variance of the amount of magnesium in the one-litre bottles.
Answer/Explanation
Markscheme
\(\bar m = \frac{{6.7 + 7.2 + \ldots + 7.3}}{{10}} = 6.91\) (M1)A1
\(s_{n – 1}^2 = \frac{1}{9}\left( {{{(6.7 – 6.91)}^2} + \ldots + {{(7.3 – 6.91)}^2}} \right)\) (M1)
\( = \frac{{0.489}}{9} = 0.0543{\text{ (3 sf)}}\) A1
Note: Award M1A0 for 0.233.
[4 marks]
Examiners report
Most candidates used a GDC to answer this question and many scored full marks in this question. However there were a significant number of candidates who showed little understanding of the meaning of unbiased estimate. In some cases, candidates wasted time by attempting to calculate the required values by hand.