Chapter 11.3, Problem 52STP

To determine

To find: The ‘Mean Score’ of 6 games.

Answer to Problem 52STP

Mean Score for 6 Games = 155.

Explanation of Solution

Given Information:

Mean Score for first 4 games = 130.

Score of 5^thGame = 180.

Score of 6^thGame = 230.

Calculation:

  $\text{Mean/Avg}\text{.=}\frac{\text{Sum of Observations}}{\text{Total Number Of Observations}}$

  $\begin{array}{l}\Rightarrow 130=\frac{\text{Total Score of 4 Games}}{4}\\ \Rightarrow 130\times 4=\text{Total Score of 4 Games}\\ \Rightarrow \text{Total Score of 4 Games}=\mathrm{520..........................................................}\left(1\right)\end{array}$

Now,

  $\text{New Mean/Avg}\text{.=}\frac{\text{Total Score Of 4 Games }\left(\text{1}\right){\text{+Score Of 5}}^{\text{th}}{\text{Game+Score Of 6}}^{\text{th}}\text{Game}}{\text{Total Number Of Games}}$

Thus,

  $\text{Mean Of 6 Games}=\frac{520+180+230}{6}$

  $\begin{array}{l}{\text{Mean}}_{\left(\text{6 Games}\right)}\text{=}\frac{\text{930}}{\text{6}}\text{=155}\\ {\text{Mean}}_{\left(\text{6 Games}\right)}\text{=155}\mathrm{.................................................................................}\left(\text{2}\right)\end{array}$

Mean Score for 6 Games = 155.