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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 ________.
48
63
64
57
63
Sum all known weights, subtract from the total sum (mean × number of observations) to find x instantly.
The weights of 9 members are 50, 63, x, 62, 64, 48, 51, 55, 48, and the mean weight is 56 kg.
Mean=n∑xi
Sum all known weights, subtract from the total sum (mean × number of observations) to find x instantly.
Counting the total number of members n incorrectly or missing one of the repeated weights like 48.
Recall Mean Formula
The mean of a dataset is calculated as the sum of all observations divided by the total number of observations, n=9.
Mean=9∑xi
Calculate Total Sum
Given the mean is 56 kg and there are 9 members, the total weight of all 9 members is 56×9.
Total Sum=56×9=504
Sum the Known Weights
Add the 8 given weights: 50+63+62+64+48+51+55+48=441.
441+x=504
Solve for x
Subtract the sum of known weights from the total sum to find the value of x.
x=504−441=57
B is correct because the sum of all 9 weights is 56×9=504, and subtracting the sum of the 8 known weights (441) gives x=57.
Problems involving missing data in statistics can always be solved by equating the total sum of observations to the product of the mean and frequency.
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