Dean Chalmers and Julian Gilbey Solutions for Chapter: Measures of Variation, Exercise 8: EXERCISE 3C

The following table shows the front tyre pressure, in psi, of five $4$-wheeled vehicles, $A$ to $E.$

Show that the variance of the pressure in all of these front tyres is $7.65{\mathrm{psi}}^2.$

The following table shows the front tyre pressure, in psi, of five $4$-wheeled vehicles, $A$ to $E.$

Rear tyre pressures for these five vehicles are denoted by $x.$ Given that $\Sigma x^2=7946$ and that the variance of the pressures in all of the front and rear tyres on these five vehicles together is $31.6275{\mathrm{psi}}^2,$ find the mean pressure in all the rear tyres.

The totals $\Sigma x^2=7931, \Sigma x=397$and $\Sigma y=499$ are given by$29$values of $x$ and $n$ values of $y.$ All the values of $x$ and $y$ together have a variance of $52.$

Express $\Sigma y^2$ in terms of $n.$

The totals $\Sigma x^2=7931, \Sigma x=397$and $\Sigma y=499$ are given by$29$values of $x$ and $n$ values of $y.$ All the values of $x$ and $y$ together have a variance of $52.$

Find the value of $n$ for which $\Sigma y^2-\Sigma x^2=10.$

The five values in a dataset have a sum of $250$ and standard deviation of $15.$  A sixth value is added to the dataset, such that the mean is now $40.$ Find the variance of the six values in the dataset.

A group of $10$ friends played a mini-golf competition. Eight of the friends tied for second place, each with a score of $34,$ and the other two friends tied for first place. Find the winning score, given that the standard deviation of the scores of all $10$ friends was $1.2$ and that the lowest score in golf wins.

An author has written $15$ children's books. The first eight books that she wrote contained between $240$ and $250$ pages each. The next six books contained between $180$ and $190$ pages each. Correct to $1$ decimal place, the standard deviation of the number of pages in the $15$ books together is $31.2.$

A set of $n$ pieces of data has mean $\overline{x}$ and standard deviation $S.$
Another set of $2n$ pieces of data has mean $\overline{x}$ and standard deviation $\frac{1}{2}S.$
Find the standard deviation of all these pieces of data together in terms of $S.$