[Math] How to find the missing sample points with the Mean and Sample Standard Deviation

data analysisstatistics

I am completely lost on this statistics question:

A statistician had a data set containing 13 data points written in his research notebook. He spilled coffee on his notebook and now he cannot read two of the data values. He remembers that the sample mean of the original data set was 26.692 and the sample standard deviaion was 10.177. Use your power of deduction and the 11 still readable data values given below, to determine the two lost data values.

Best Answer

You can set up a system of equations, denote the two missing data points by x and y, then the formula for the mean gives you one equation involving x and y and the one for the standard deviation gives you a second one. Then you have to solve this system of two equations for x and y.

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