Determine by calculation, the median and interquartile range?

Question

Time-----------Frequency
(nearest hour)
0-4--------------------66
5-9--------------------51
10-14-----------------12
15-19-----------------6
20-24-----------------3
25-29-----------------2
Determine by calculation, the median and interquartile range.

Answer 1

You have 66+51+12 +6+3+2 = 140 data values. So the median is the mean of 70th and 71st data value (69 above and 69 below). This is "somewhere" in the range 5-9. In this situation it is recommended that you take the mid-point 7 as the data value: median =7. For the quartiles you cut it up in fourths: Q1 at 1/4*140 = 35 so the 35th data value is in the range 0-4 so use the value 2 while Q3 at 3/4*140 = 105 so the 105th data value is in the range 5-9 so use the value 7. IQR is then Q3-Q1 = 7-2 = 5. This topic is called "grouped data," the formulas *look* confusing but are trying to express a "no-duh" idea: if you don't have the original data, default to the mid-point. Advice (if you use stats in your career): don't lose the original data. Haha!

Answer 2

The best way to do this would be to plot a graph od time against frequency. It becomes easy to see once that is done.
The median would be the value at the 50th time percentile and the interquartile range would be the difference between the 75th percentile time value and the 25th percentile time value.