For a certain distribution, 10.0 is one standard deviation above the mean, and 13.0 is three standard deviations above the mean. What is the mean of the data set?
Question
For a certain distribution, 10.0 is one standard deviation above the mean, and 13.0 is three standard deviations above the mean. What is the mean of the data set?
Solution
To find the mean of the data set, we first need to determine the value of the standard deviation.
Given that 10.0 is one standard deviation above the mean, and 13.0 is three standard deviations above the mean, we can set up the following equations:
Mean + 1(Standard Deviation) = 10.0 Mean + 3(Standard Deviation) = 13.0
Subtract the first equation from the second to get:
2(Standard Deviation) = 3.0
So, the Standard Deviation = 3.0 / 2 = 1.5
Now, substitute the Standard Deviation back into the first equation:
Mean + 1(1.5) = 10.0 Mean = 10.0 - 1.5 = 8.5
So, the mean of the data set is 8.5.
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