A01ans - EXERCISES IN STATISTICS Series A, No. 1 1. The...

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EXERCISES IN STATISTICS Series A, No. 1 1. The number of children recorded to each of 25 families were 2 , 4 , 1 , 0 , 1 , 3 , 0 , 4 , 2 , 6 , 0 , 0 , 2 , 3 , 1 , 5 , 4 , 0 , 3 , 1 , 2 , 5 , 3 , 4 , 1 . (a) Construct a frequency table and a graph for the distribution of family size in this sample. (b) Find the sample mean and the standard deviation. Answer: x i f i f i x i x 2 i f i x 2 i 0 IIIII 5 0 0 0 1 5 5 1 5 2I I I I 4 8 4 1 6 3 IIII 4 12 9 36 4 4 16 16 64 5 II 2 10 25 50 6 I 1 6 36 36 25 57 207 f i f i x i f i x 2 i We ±nd that Mean = f i x i f i = fix i N = 57 25 =2 . 28 We can say that the average number of children per family is 2.28. One should take care to state this correctly. For example, it is absurd to say that “The average family has 2.28 children”. We also ±nd that Variance = f i ( x i ¯ x ) 2 N = f i x 2 i N µ ∑ f i x i N 2 = 207 25 µ 57 25 2 =3 . 082 1
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SERIES A No.1 : ANSWERS 2. Find expressions in terms of the mean and variance of x for (a) the mean and variance of y = ax , (b) the mean and variance of y = ax + b .
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This note was uploaded on 03/02/2012 for the course EC 2019 taught by Professor D.s.g.pollock during the Spring '12 term at Queen Mary, University of London.

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A01ans - EXERCISES IN STATISTICS Series A, No. 1 1. The...

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