# Finding measure of dispersion

Given a data set as follows:

$$\begin{array}{crrrrrrrr} Classes: & Less\:than\:20 & 20-30 & 30-40 & 40-50 & 50-60 \\ frequency: & 30 & 20 & 15 & 10 & 5 \end{array}$$

The objective is to find a suitable measure of dispersion.

The first thing I thought of was the variance, but can we find out the mid point of a class interval without the lower point ?

Then, I thought of quartile range, but the lower quartile lies in the first class only, so couldn't proceed further.

Next range, again lower and upper limits required.

Can anyone help me with this ? Any suggestions on what measure of dispersion could be used ?

• Selecting one's statistic based on reviewing the data is a dicey procedure. For exploratory analysis it's fine, but for almost anything else it is difficult to justify. Could you explain what this measure of dispersion will be used for? You might also explain how the class cutpoints were selected (do they depend on the data, too?) and provide a lower limit for the open-ended "less than 20" class.
– whuber
May 18, 2017 at 13:15
• Is the number of observations in the class "greater than 60" equal to zero or do you have right truncated data, that is, the number of observations in this class is unkown? May 18, 2017 at 13:59