The weights (in kg) of 9 members of a school cricket team are 50, 63, x, 62, 64, 48, 51, 55, 48. If the mean weight is 56 kg, then the value of x is:
63
Finding the Unknown Weight (x) in a Cricket Team Using Mean
This problem involves finding a missing value in a dataset when the mean (average) is known. We are given the weights of 9 members of a school cricket team, with one weight represented by the variable x. We know the mean weight of the team.
Understanding the Concept of Mean
The mean, or average, of a set of numbers is calculated by summing all the numbers in the set and then dividing by the count of numbers in the set.
The formula for the mean is:
\( \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \)
Applying the Formula to the Problem
We are given the following information:
- Weights (in kg): 50, 63, x, 62, 64, 48, 51, 55, 48
- Number of members (observations) = 9
- Mean weight = 56 kg
Step-by-Step Calculation
- Calculate the sum of the known weights:
Sum = 50 + 63 + 62 + 64 + 48 + 51 + 55 + 48
Sum = 441 kg
- Calculate the total sum of all weights using the mean:
Total Sum = Mean weight \(\times\) Number of members
Total Sum = \(56 \times 9\)
Total Sum = 504 kg
- Set up the equation to find x:
The total sum of weights is also the sum of the known weights plus the unknown weight (x).
Total Sum = Sum of known weights + x
\( 504 = 441 + x \)
- Solve for x:
Subtract the sum of known weights from the total sum.
\( x = 504 - 441 \)
\( x = 63 \)
Conclusion
The value of x, representing the missing weight, is 63 kg. This means the weights of the 9 team members are 50, 63, 63, 62, 64, 48, 51, 55, and 48 kg.
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