The average runs of a cricket player of 10 innings were 40. How many runs must she make in her next inning so as to increase her average of runs by 3?
73
Calculating Runs Needed to Increase Cricket Average
This question asks us to determine the number of runs a cricket player must score in their eleventh inning to increase their average runs by 3, given their average over the first 10 innings.
Understanding Cricket Average
The average runs of a cricket player is calculated by dividing the total runs scored by the number of innings played.
Formula for Average Runs:
Average Runs = Total Runs / Number of Innings
Step-by-Step Calculation
Step 1: Calculate the Total Runs in the First 10 Innings
We are given that the average runs over 10 innings is 40.
Using the formula:
Average Runs = Total Runs / Number of Innings
We can find the Total Runs:
Total Runs = Average Runs × Number of Innings
Given:
- Average Runs = 40
- Number of Innings = 10
Total Runs in 10 innings = $40 \times 10 = 400$ runs.
Step 2: Determine the Desired New Average
The player wants to increase her average by 3 runs in the next inning.
Initial Average = 40
Increase in Average = 3
Desired New Average = Initial Average + Increase in Average
Desired New Average = $40 + 3 = 43$ runs.
Step 3: Determine the Total Innings After the Next Match
The player has played 10 innings and is about to play her next (11th) inning.
Total Innings After Next Match = 10 + 1 = 11 innings.
Step 4: Calculate the Desired Total Runs After 11 Innings
To achieve a new average of 43 over 11 innings, we can use the average formula again:
Total Runs = Desired New Average × Total Innings After Next Match
Given:
- Desired New Average = 43
- Total Innings After Next Match = 11
Desired Total Runs after 11 innings = $43 \times 11$
Let's calculate $43 \times 11$:
$43 \times 11 = 43 \times (10 + 1) = 43 \times 10 + 43 \times 1 = 430 + 43 = 473$ runs.
So, the total runs after 11 innings should be 473.
Step 5: Calculate the Runs Needed in the 11th Inning
The runs in the 11th inning is the difference between the desired total runs after 11 innings and the total runs after the first 10 innings.
Runs in 11th Inning = Desired Total Runs after 11 innings - Total Runs in 10 innings
Runs in 11th Inning = $473 - 400$
Runs in 11th Inning = $73$ runs.
Therefore, the player must score 73 runs in her next inning to increase her average of runs by 3.
| Parameter | Value |
|---|---|
| Initial Average (10 innings) | 40 |
| Total Runs (10 innings) | $40 \times 10 = 400$ |
| Desired Average (11 innings) | $40 + 3 = 43$ |
| Desired Total Runs (11 innings) | $43 \times 11 = 473$ |
| Runs in 11th Inning | $473 - 400 = 73$ |
Revision Table: Cricket Average Calculation
| Concept | Description | Formula |
|---|---|---|
| Average | Sum of observations divided by the number of observations. | Average = $\frac{\text{Sum}}{\text{Count}}$ |
| Total Runs | Sum of runs scored in all innings. | Total Runs = Average × Innings |
| Runs in Next Inning (to change average) | (New Average $\times$ New Number of Innings) - (Old Average $\times$ Old Number of Innings) | Runs = $(\text{Avg}_{\text{new}} \times N_{\text{new}}) - (\text{Avg}_{\text{old}} \times N_{\text{old}})$ |
Additional Information: Importance of Average in Cricket
Cricket average is a key statistic used to evaluate the performance of batsmen and bowlers. For batsmen, a higher average indicates consistent scoring. For bowlers, a lower average (runs conceded per wicket) indicates effectiveness. Calculating how runs in a single inning can impact the overall average is a common analytical task in cricket statistics.
Understanding the relationship between total runs, number of innings, and average allows players and analysts to set performance goals and track progress.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
