Calculating Combined Average Runs
The problem requires finding the overall average runs scored by a batsman across 33 matches.
We are given:
- Average runs in the first 23 matches = 43 runs.
- Average runs in the next 10 matches = 16 runs.
- Total number of matches = 33.
Step-by-Step Solution
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Calculate the total runs scored in the first 23 matches.
Total Runs (first 23 matches) = Number of matches $\times$ Average runs
Total Runs = $23 \times 43 = 989$ runs.
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Calculate the total runs scored in the next 10 matches.
Total Runs (next 10 matches) = Number of matches $\times$ Average runs
Total Runs = $10 \times 16 = 160$ runs.
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Calculate the total runs scored in all 33 matches.
Overall Total Runs = Total Runs (first 23) + Total Runs (next 10)
Overall Total Runs = $989 + 160 = 1149$ runs.
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Calculate the combined average runs scored in all 33 matches.
Combined Average = $\frac{\text{Overall Total Runs}}{\text{Total Number of Matches}}$
Combined Average = $\frac{1149}{33}$
Combined Average $\approx 34.8181...$ runs.
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Round the combined average to two decimal places.
Rounded Average = $34.82$ runs.
Final Answer
The average runs scored by the batsman in all 33 matches, rounded to two decimal places, is 34.82.
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