Question : The given histogram represents the frequency distribution of average runs scored by 50 selected players from a district in a local cricket tournament.
What is the overall average score of the 50 players?
Option 1: 29.3
Option 2: 38.5
Option 3: 32.6
Option 4: 37.1
Correct Answer: 37.1
Solution :
The sum of runs scored by all 50 players
= $\frac{10.5+20.5}{2}\times 6 + \frac{20.5+30.5}{2} \times 10 + \frac{30.5+40.5}{2} \times 12 + \frac{40.5+50.5}{2} \times 16 + \frac{50.5+60.5}{2} \times 4 + \frac{60.5+70.5}{2} \times 2$
= $\frac{31}{2}\times 6 + \frac{51}{2} \times 10 + \frac{71}{2} \times 12 + \frac{91}{2} \times 16 + \frac{111}{2} \times 4 + \frac{131}{2} \times 2$
= 93 + 255 + 426 + 728 + 222 + 131
= 1855
Average runs made by all 50 players = $\frac{1855}{50}$
= 37.1
Hence, the correct answer is 37.1
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