Respuesta :
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 [tex]$ \textbf{B}_{\textbf{i} $[/tex], where [tex]$ i = 1, 2, 3, \hdots, 11 $[/tex] denote the batsmen.
From the first statement, we have:
[tex]$ \frac{B_1 + B_2 + B_3 + B_4}{4} = 42.5 $[/tex]
[tex]$ \implies B_1 + B_2 + B_3 + B_4 = 42.5 \times 4 = \textbf{170} $[/tex]
Therefore, the sum of the scores of the first four batsmen is 170.
Now, from the second statement we have:
[tex]$ \frac{B_5 + B_6 + B_7 + B_8 + B_9 + B_{10} + B_{11}}{7} = 18 $[/tex]
[tex]$ \implies B_5 + B_6 + B_7 + B_8 + B_9 + B_{10} + B_{11} = 18 \times 7 = \textbf{126} $[/tex]
That is, the sum of the scores of the remaining 7 batsmen is 126.
Now, to calculate the average(mean) of the entire team, we add the individual scores and divide it by 11.
[tex]$ \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} $[/tex]
[tex]$ = \frac{296}{11} $[/tex]
[tex]$ = \textbf{26.90} $[/tex] which is the required answer.
