Given that the mean number of goals scored per player is \(1.95\) , find the value of \(k\).

It is discovered that there is a mistake in the data and that the top scorer, who scored 22 goals, has not been included in the table.

(i)     Find the correct mean number of goals scored per player.

(ii)     Find the correct standard deviation of the number of goals scored per player.

\(\frac{{0 \bullet 4 + 1 \bullet k + 2 \bullet 3 + 3 \bullet 2 + 4 \bullet 3 + 8 \bullet 1}}{{13 + k}} = 1.95\;\;\;\left( {\frac{{k + 32}}{{k + 13}} = 1.95} \right)\)     (M1)

attempting to solve for \(k\)     (M1)

\(k = 7\)     A1

[3 marks]

(i)     \(\frac{{7 + 32 + 22}}{{7 + 13 + 1}} = 2.90\;\;\;\left( { = \frac{{61}}{{21}}} \right)\)     (M1)A1

(ii)     standard deviation \( = 4.66\)     A1

Note:     Award A0 for \(4.77\).

[3 marks]

Total [6 marks]