Twenty values of x are summarised by (x 1) 2 = 132 and (x 1) =

Twenty values of x are summarised by ­Σ(x −1)² = 132 and ­ Σ(x −1) = 44.

Eighty values of y are summarised by Σ­(y +1)² = 17 704 and Σ­(y +1) = 1184.

a. Show that Σ­x = 64 and that Σ­x² = 240.

b. Calculate the value of Σ­y and of Σ­.

Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c. The number of goals scored in the past 15 matches are summarised by ­Σ(u −1)² = 25, ­ Σ(u −1) = 9, Σ­c² = 39 and Σ­c = 19.

a. How many goals have been scored altogether in these 15 matches?

b. Show that Σ­u² = 58.

c. Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.

y².

c. Find the exact variance of the 100 values of x and y combined.