Question

52. A cricketer has an average of 28 runs in 24 innings. How many runs must he score in the 25 inning to make his average 29 ?​

Answer 1

Answer:

53 runs

Step-by-step explanation:

So technically, average is the numbers added divided by how many numbers.

So we have an average of 28 with 24 numbers. (24 numbers added together and divided by 24 is 28).

If we want to find the original number before we divided by 24, we would do times 24.

So, 28 × 24 = 672

Next, we need an average of 29 with 25 numbers.

So if we multiply those, we get 725.

Lastly, right now, there is a total of 674 runs, and we need 725 runs.

So for that, we have to subtract it.

725 - 672 = 53

Hence, the cricketer needs 53 more runs in the last inning.

Answer 2

Concept:

Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.

Given:
A cricketer has an average of 28 runs in 24 innings.

Find:
How much should he score in the 25th inning to make an average of 29 runs.

Solution:

As the cricketer has an average of 28 runs in 24 innings he has
$\[ \dfrac{\sum_{i=1}^{i=24} x_i}{24} =28\]$
where $x_i$ is the number of runs at $i^{\mbox{th}}$ inning.  
Suppose that the cricketer scores x runs in the 25th inning then

$\[\dfrac{ x+\sum_{i=1}^{i=24} x_i}{25} =29\]$

Now, we know from the first equation that

$\sum_{i=1}^{i=24} x_i = 28\times 24 = 672$

⇒ $\[\dfrac{ x+672}{25} =29\]$

⇒ x = 25×29 - 672 = 53

Hence, the cricketer must score 53 runs to have an average of 29 runs at the end of 25 innings.

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