Answer to Question #289714 in Statistics and Probability for Zia

Question

The raw data has been organised in the frequency table below.

games frequency

6 2

7 5

8 n

9 4

10 4

11 2

12 2

13 2

(a) Write down the value of n.

(b) Calculate the mean number of games played per set.

(c) What percentage of the sets had more than 10 games?

(d) What is the modal number of games?

Answer 1

The numbers of games played in each set of a tennis tournament were

$$9,7,8,11,9,6,10,8,12,6,8,13,7,$$

$$9,10,9,10,11,12,8,7,13,10,7,7$$

The raw data has been organised in the frequency table below.

$$\def\arraystretch{1.5} \begin{array}{c:c} games & frequency \\ \hline 6 & 2\\ \hdashline 7 & 5\\ \hdashline 8 & n\\ \hdashline 9 & 4\\ \hdashline 10 & 4\\ \hdashline 11 & 2\\ \hdashline 12 & 2\\ \hdashline 13 & 2\\ \hdashline \end{array}$$

(a) $n=4$

(b)

$$mean=\dfrac{1}{2+5+4+4+4+2+2+2}\big(6(2)+7(5)$$

$$+8(4)+9(4)+10(4)+11(2)+12(2)+13(2)\big)=$$

$$=9.08$$

(c)

$$\dfrac{2+2+2}{25}\times100\%=24\%$$

(d) The modal number of games is 7 (five times).