Data Management median, interquile and semi-interquile question

[triselle]

The Nurses' union collects data on the hours worked by operating-room nurses at the Stratsville General Hospital.

This is the chart:

Hours per week	Number of Employees
12	1
32	5
35	7
38	8
42	5

b) Determine the median, interquile range, and semi-interquile range.


I have no idea no idea to do this question

can any one help??? thanks

 

[JeffM]

The Nurses' union collects data on the hours worked by operating-room nurses at the Stratsville General Hospital.

This is the chart:

Hours per week	Number of Employees
12	1
32	5
35	7
38	8
42	5

b) Determine the median, interquile range, and semi-interquile range.


I have no idea no idea to do this question

can any one help??? thanks

If you click on the word median in color above, you will get a little lesson on the median. See whether you are confident of your answer after reading that. If you are not confident, please tell us what your answer is and why you are unsure about it. As for the rest of the question, what EXACTLY does your problem ask? Interquile range??????

 

[triselle]

If you click on the word median in color above, you will get a little lesson on the median. See whether you are confident of your answer after reading that. If you are not confident, please tell us what your answer is and why you are unsure about it. As for the rest of the question, what EXACTLY does your problem ask? Interquile range??????

I know what median means, it's just turns out I'm having trouble trying to find the answer.
The answer at the back of the text book says 36.5 for the median

I'm not sure how that answer came to be, but I do understand the rest of the homework this is the only one I don't understand.

 

[JeffM]

I know what median means, it's just turns out I'm having trouble trying to find the answer.
The answer at the back of the text book says 36.5 for the median

I'm not sure how that answer came to be, but I do understand the rest of the homework this is the only one I don't understand.

Ahh OK. I see what your problem is.

The number of observations or experiments or data points is

\(\displaystyle 1 + 5 + 7 + 8 + 5 = 26.\)

What is half of 26? 13. If we split the observations into two sorted groups of 13, we find 13 with values of 35 or fewer hours and 13 with values of 38 hours or more. If we say the central value is 35 hours, there will be 6 observations with values below 35 and 13 observations with values above 35. So 35 cannot be the central value. If we say the central value is 38 hours, there will be 5 observations with values above 38 and 13 observations with values below 38. So 38 cannot be the central value. Now we see that any value more than 35 but fewer than 38 is a central value in the sense that there will be an equal number of values above and an equal number of values below. But if we choose a value closer to 35 than 38, that choice implies that the values lean more toward 35 than 38. If on the other hand we choose a value closer to 35 than 38, that choice implies that the values lean more toward 38 than 35. So both those choices imply something that is not observed in the data. If we choose the mean between 35 and 38, which is 36.5, and call that the central value, then it is true that we have an equal number of observations above and below the central value, and we have not implied that 35 is a better choice than 38 or vice versa. We have been exact and unbiased.