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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 57 kg, then the value of x is ________.
64
72
57
63
72
Calculate the difference of each value from the assumed mean (57). (50-57)=-7, (63-57)=6, (62-57)=5, (64-57)=7, (48-57)=-9, (51-57)=-6, (55-57)=-2, (48-57)=-9. Sum of these = -15. Since total deviation must be 0, (x-57) - 15 = 0, so x = 57 + 15 = 72.
Number of members n = 9. The weights are 50, 63, x, 62, 64, 48, 51, 55, 48. Mean weight = 57 kg.
Mean=n∑xi
Calculate the difference of each value from the assumed mean (57). (50-57)=-7, (63-57)=6, (62-57)=5, (64-57)=7, (48-57)=-9, (51-57)=-6, (55-57)=-2, (48-57)=-9. Sum of these = -15. Since total deviation must be 0, (x-57) - 15 = 0, so x = 57 + 15 = 72.
Missing one of the digits in the sum calculation (e.g., forgetting to count the duplicate '48' twice).
Calculate sum of known weights
Add the 8 provided weights together: 50+63+62+64+48+51+55+48.
50+63+62+64+48+51+55+48=441
Find total sum using Mean formula
Given the mean of 9 members is 57, the total sum is 9×57.
9×57=513
Solve for x
Subtract the sum of the 8 members from the total sum: x=513−441.
x=72
B is correct because the sum of the 9 members must be 9×57=513, and subtracting the known sum of 441 gives x=72.
This type of 'missing value' problem appears frequently in Statistics and Data Interpretation sections of competitive exams.
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