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If the mean of 5, 10, 15, x, 25 is 15, find x.
15
20
25
10
20
Use the property of mean: the sum of deviations of all values from their mean is zero, so (5-15) + (10-15) + (15-15) + (x-15) + (25-15) = 0.
The given observations are 5, 10, 15, x, and 25, and their mean is 15.
Mean=nтИСxiтАЛтАЛ
Use the property of mean: the sum of deviations of all values from their mean is zero, so (5-15) + (10-15) + (15-15) + (x-15) + (25-15) = 0.
Forgetting to divide by the total number of observations or making arithmetic errors while summing numbers.
Write the formula for mean
The mean of a set of observations is given by the formula: Mean=Number┬аof┬аobservationsSum┬аof┬аobservationsтАЛ
Mean=nтИСxтАЛ
Substitute the given values
Here, the observations are 5,10,15,x,25, the number of observations n=5, and the mean is 15.
15=55+10+15+x+25тАЛ
Simplify the numerator
Add the known numerical terms together in the numerator: 5+10+15+25=55.
15=555+xтАЛ
Solve for x
Multiply both sides by 5 to get 75=55+x, and then subtract 55 from both sides to find x.
x=75тИТ55=20
B is correct because the calculated value of x is 20.
Understanding the properties of mean and deviations helps save time in data interpretation and statistics questions in competitive exams.
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