Thread: Statistical analysis: determining median

I know that to determine the median or quartile positions of grouped data I have to plot a cumulative frequecy graph by plotting the accummulated frequency against the upper-class boundary of the class(group). If the data is not grouped I can find the median exactly by counting the number of data and determining the positon of the median by whether the number of data is odd or even.
Q.
The lengths of 120 nails of nominal length 3cm were measured, each correct to the nearest 0.05cm. The results are summarised in the following table.

Length 2.85 2.90 2.95 3.00 3.05 3.10 3.15
Frequency 1 11 27 41 26 12 2

a) Draw a box-whisker plot of these results, taking the extremes as 2.825cm and 3.175cm

My problem is, what should I do now that continuous data has been rounded off? Should I treat it as grouped data and plot a cumulative frequency graph or just find the median by 120 / 2 = 60, half way between the 60th and 61st value??
The second method is when you know the exact value of each measurement, but it is continuous and rounded off so I don't. But the class is just a single value so I think a cumulative graph is over-kill.
I know how to apply either method but I don't know which is best for this particular situation. Is there are standard practice for this type of situation?

Thanks

Originally Posted by woollybull

I know that to determine the median or quartile positions of grouped data I have to plot a cumulative frequecy graph by plotting the accummulated frequency against the upper-class boundary of the class(group). If the data is not grouped I can find the median exactly by counting the number of data and determining the positon of the median by whether the number of data is odd or even.
Q.
The lengths of 120 nails of nominal length 3cm were measured, each correct to the nearest 0.05cm. The results are summarised in the following table.

Length 2.85 2.90 2.95 3.00 3.05 3.10 3.15
Frequency 1 11 27 41 26 12 2

a) Draw a box-whisker plot of these results, taking the extremes as 2.825cm and 3.175cm

My problem is, what should I do now that continuous data has been rounded off? Should I treat it as grouped data and plot a cumulative frequency graph or just find the median by 120 / 2 = 60, half way between the 60th and 61st value??
The second method is when you know the exact value of each measurement, but it is continuous and rounded off so I don't. But the class is just a single value so I think a cumulative graph is over-kill.
I know how to apply either method but I don't know which is best for this particular situation. Is there are standard practice for this type of situation?

Thanks

You have a table of data. Find the median and other quartiles in the usual way. The median is the average of the 60th and 61st ordered data values etc.

Thanks and Happy New Year!