Question

There are 30 teams in Major League Baseball, five of which play in California. Last year, the average number of home runs hit by all teams in the league was 187. The average number of home runs hit by the California teams was 164.2. What was the average number of home runs hit by the other 25 teams?

Answer 1

The average number of home runs hits by 25 other teams was "191.56".

According to the question,

Number of teams,

• 30

Combined mean,

• $\bar x_c = 187$

Let, the teams average be "$\bar x_1$"

• $\bar x_1 = 164.2$
• $n_1 = 5$
• $n_2 = 25$

As we know, the formula for combined mean will be:

→ $\bar x_c = \frac{n_1 \bar x_1 + n_2 \bar x_2 }{n_1+n_2}$

By substituting the values, we get

→ $187 = \frac{5(164.2)+ 25 \bar x_2}{5+25}$

→ $187 = \frac{821+25 \bar x_2}{30}$

→ $5610=821+25 \bar x_2$

→ $25 \bar x_2 = 5610-821$

→     $\bar x_2 = \frac{4789}{25}$

→          $= 191.56$

Thus the above solution is right.

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