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Review exercise 1, Number 19:

A consumer group is investigating telephone usage within a particular city. The numbers of telephone units, x, used in a particular quarter by a random sample of 250 households were summarised in a group frequency table. In order to simplify the arithmetic the data in the table were coded such that :
y=x-290 / 10, giving (Sigma symbol)fy=-40 and (sigma symbol)fy^2=1075
a) Find estimates of the mean and the variance of the number of telephone units used in that quarter by households in the city.

How do I do this Question?
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Jonny W
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You need to know the following results. They are valid for any random variable X and any numbers a and b.

E(aX + b) = a E(X) + b
Var(aX + b) = a^2 Var(X)

--

Let X be the telephone usage of a randomly selected household in the city. Let Y be the coded telephone usage of that household.

Then Y = (X - 290)/10. So X = 10Y + 290.

E(X) = 10 E(Y) + 290
Var(X) = 10^2 Var(Y) = 100 Var(Y)

Estimate E(Y) and Var(Y) using the data. Then use the above formulas to estimate E(X) and Var(X).
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