Answer:
The mean score of the entire team is 26.909.
Step-by-step explanation:
Given that four batsmen had a mean of 42.5.
Let
, where
denote the batsmen.
From the first statement, we have:
![$ \frac{B_1 + B_2 + B_3 + B_4}{4} = 42.5 $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7BB_1%20%2B%20B_2%20%2B%20B_3%20%2B%20B_4%7D%7B4%7D%20%3D%2042.5%20%24)
![$ \implies B_1 + B_2 + B_3 + B_4 = 42.5 \times 4 = \textbf{170} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20B_1%20%2B%20B_2%20%2B%20B_3%20%2B%20B_4%20%3D%2042.5%20%5Ctimes%204%20%3D%20%20%5Ctextbf%7B170%7D%20%24)
Therefore, the sum of the scores of the first four batsmen is 170.
Now, from the second statement we have:
![$ \frac{B_5 + B_6 + B_7 + B_8 + B_9 + B_{10} + B_{11}}{7} = 18 $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7BB_5%20%2B%20B_6%20%2B%20B_7%20%2B%20B_8%20%2B%20B_9%20%2B%20B_%7B10%7D%20%2B%20B_%7B11%7D%7D%7B7%7D%20%3D%2018%20%24)
![$ \implies B_5 + B_6 + B_7 + B_8 + B_9 + B_{10} + B_{11} = 18 \times 7 = \textbf{126} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20B_5%20%2B%20B_6%20%2B%20B_7%20%2B%20B_8%20%2B%20B_9%20%2B%20B_%7B10%7D%20%2B%20B_%7B11%7D%20%3D%2018%20%5Ctimes%207%20%3D%20%5Ctextbf%7B126%7D%20%24)
That is, the sum of the scores of the remaining 7 batsmen is 126.
Now, to calculate the average(mean) of the entire team, we add the individual scores and divide it by 11.
![$ \implies \frac{B_1 + B_2 + B_3 + B_4 + B_5 + B_6 + B_7 + B_8 + B_9 + B_{10} + B_{11}}{11} = \frac{170 + 126}{11} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20%5Cfrac%7BB_1%20%2B%20B_2%20%2B%20B_3%20%2B%20B_4%20%2B%20B_5%20%2B%20B_6%20%2B%20B_7%20%2B%20B_8%20%2B%20B_9%20%2B%20B_%7B10%7D%20%2B%20B_%7B11%7D%7D%7B11%7D%20%3D%20%5Cfrac%7B170%20%2B%20126%7D%7B11%7D%20%24)
![$ = \frac{296}{11} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B296%7D%7B11%7D%20%24)
which is the required answer.