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If the mean of 22, 25, 27, 24 and x is 26, then the value of x is:
35
28
32
41
32
Calculate the deviation of each given number from the target mean (26): (22-26 = -4, 25-26 = -1, 27-26 = +1, 24-26 = -2). The sum of deviations is -4 - 1 + 1 - 2 = -6. Since the sum of deviations from the mean must be zero, xтИТ26=+6тЯ╣x=32.
Given numbers: 22,25,27,24, and x. Number of observations n=5. Mean = 26.
Mean=Number┬аof┬аobservationsSum┬аof┬аall┬аobservationsтАЛ
Calculate the deviation of each given number from the target mean (26): (22-26 = -4, 25-26 = -1, 27-26 = +1, 24-26 = -2). The sum of deviations is -4 - 1 + 1 - 2 = -6. Since the sum of deviations from the mean must be zero, xтИТ26=+6тЯ╣x=32.
Forgetting to include x in the count of total observations (n=5) or making calculation errors while summing the numbers.
Recall the formula for mean
The mean of a set of observations is calculated by dividing the sum of all the observations by the total number of observations.
Mean=nSum┬аof┬аobservationsтАЛ
Set up the equation
Given the numbers 22,25,27,24 and x, total count n=5, and mean =26. Substitute these values into the formula.
522+25+27+24+xтАЛ=26
Calculate the sum of known numbers
Add the known numerical values in the numerator: 22+25+27+24=98.
598+xтАЛ=26
Solve for x
Multiply both sides by 5 to clear the denominator, then isolate x.
98+x=26├Ч5=130тЯ╣x=130тИТ98=32
C is correct because the calculated value of x is 32.
Similar average-based problems frequently appear in quantitative aptitude where missing frequencies or missing values in grouped or ungrouped data need to be determined.
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