Calculating the Average Score in Cricket Matches

This problem asks us to find the combined average score of a cricketer over five matches. We are given the average score for the first three matches and the average score for the next two matches. To find the overall average, we need to calculate the total runs scored across all five matches and then divide by the total number of matches.

Average Score Basics

Remember that the average (or mean) is calculated by summing up all the values and dividing by the count of those values. Mathematically,

$$ \text{Average} = \frac{\text{Sum of Values}}{\text{Number of Values}} $$

From this, we can also find the sum of values if we know the average and the number of values:

$$ \text{Sum of Values} = \text{Average} \times \text{Number of Values} $$

Step 1: Calculate Total Runs in the First Three Matches

The average score in the first three matches is given as 38.

Using the formula above:

Total Runs (3 matches) = Average Score $\times$ Number of Matches

$$ \text{Total Runs}_{\text{3 matches}} = 38 \times 3 $$

$$ \text{Total Runs}_{\text{3 matches}} = 114 $$

So, the cricketer scored a total of 114 runs in the first three matches.

Step 2: Calculate Total Runs in the Other Two Matches

The average score in the next two matches is given as 23.

Using the same formula:

Total Runs (2 matches) = Average Score $\times$ Number of Matches

$$ \text{Total Runs}_{\text{2 matches}} = 23 \times 2 $$

$$ \text{Total Runs}_{\text{2 matches}} = 46 $$

The cricketer scored a total of 46 runs in these two matches.

Step 3: Calculate Total Runs in All Five Matches

To find the total runs scored in all five matches, we add the total runs from the first set of matches and the second set:

Total Runs (5 matches) = Total Runs (3 matches) + Total Runs (2 matches)

$$ \text{Total Runs}_{\text{5 matches}} = 114 + 46 $$

$$ \text{Total Runs}_{\text{5 matches}} = 160 $$

The cricketer scored a total of 160 runs in all five matches.

Step 4: Calculate the Average Score in All Five Matches

Now, we calculate the overall average score using the total runs scored in all five matches and the total number of matches.

Overall Average Score = $\frac{\text{Total Runs (5 matches)}}{\text{Total Number of Matches}}$

The total number of matches is $3 + 2 = 5$.

$$ \text{Average}_{\text{5 matches}} = \frac{160}{5} $$

$$ \text{Average}_{\text{5 matches}} = 32 $$

Therefore, the average score of the cricketer in all five matches is 32.