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In the Assumed Mean Method, if the assumed mean (A) = 55 and an observed value x = 40, what is the deviation d?
1.5
1.5
15
15
15
Simply subtract the assumed mean from the observed value. Since 40 is less than 55, the result must be negative.
Assumed mean (A) = 55, Observed value (x) = 40.
d=xтИТA
Simply subtract the assumed mean from the observed value. Since 40 is less than 55, the result must be negative.
Students often calculate AтИТx instead of xтИТA, leading to the incorrect positive value 15.
Identify the variables
Identify the given values from the question: the observed value x=40 and the assumed mean A=55.
x=40,A=55
Apply the deviation formula
Substitute the given values into the standard deviation formula for the Assumed Mean Method: d=xтИТA.
d=40тИТ55
Calculate the final result
Perform the subtraction to find the deviation d.
d=тИТ15
D is correct because subtracting the assumed mean of 55 from the observed value of 40 yields a deviation of -15.
Understanding deviations is fundamental to calculating variance and standard deviation in statistics; remember that negative deviations are just as valid as positive ones.
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