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The mean of 10, 12, 15, 18, and x is 15. Find x.
18
20
25
15
20
Calculate the deviation of each number from the mean 15. The deviations are (10-15)=-5, (12-15)=-3, (15-15)=0, (18-15)=+3. The sum of these deviations is -5. Since the total deviation must be 0, the deviation for x must be +5. Therefore, x = 15 + 5 = 20.
Data points are 10, 12, 15, 18, and x. The mean of these 5 observations is 15.
Mean=nтИСxiтАЛтАЛ
Calculate the deviation of each number from the mean 15. The deviations are (10-15)=-5, (12-15)=-3, (15-15)=0, (18-15)=+3. The sum of these deviations is -5. Since the total deviation must be 0, the deviation for x must be +5. Therefore, x = 15 + 5 = 20.
Students often forget to include the unknown variable x in the count of observations (n=5 instead of n=4).
Define the Mean Formula
The mean is calculated by dividing the sum of all observations by the number of observations (n). Here, n=5.
Mean=510+12+15+18+xтАЛ
Set up the Equation
Equate the sum expression to the given mean value of 15.
15=555+xтАЛ
Solve for x
Multiply both sides by 5 and solve the resulting linear equation.
75=55+xтЯ╣x=75тИТ55=20
B is correct because the calculation yields x = 20, which matches option B.
This concept of 'sum of deviations from the mean being zero' is a foundational principle in Statistics and is very useful in calculating the Variance and Standard Deviation quickly.
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