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I have a set of data in exclusive form. The Time(class limit) is from 0-20, 20-40, 40-60, 60-80 and 80-100. The frequency in bracket of each classes are as follow 0-20(f=2), 20-40(f=15), 40-60(f=20), 60-80(F=10), 80-100(f=3).

I was asked to find the mean and median and standard deviation of this data. The mean was 48.8. I divide the total sum of (frequency × midpoint) 2440 by total frequency sum which is 50. Now for the median. I am not sure how to calculate my class boundaries. Can class boundaries here be zero? if so will my first class boundary be -0.5 - 19.5? and my second class boundary 19.5 - 39.5?

Sasha Bambi
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  • You have 50 observations. Clearly the median is in interval '40-60' because seventeen observations lie below 40 and another twenty are in that interval. Assume observations are uniformly spread through '40-60' and interpolate. Roughly, you need eight more observations to reach twenty-five; that's $8/20$ of the way into '40-60', so an estimate for the median is 48. Most elementary stat books have a formula to implement someone's precise version of the interpolation. // You are correct that you need so know whether, say, the 2nd interval is really $[20, 40),; (20,40],$ or $(19.5, 39.5),$ etc. – BruceET Nov 17 '17 at 05:32

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