Question

What is the mean, median, mode, and range of 5, 30, 35, 20, 5, 25, 20?

Answer 1

Mean, Median and Mode all are `20`. Range is `30`.

Explanation:

Mean of `5, 30, 35, 20, 5, 25, 20` is simple average of these numbers i.e. `(5+30+35+20+5+25+20)/7` or `140/7` i.e. `20`.

For finding median arrange them in increasing or decreasing order and middle term is mode. In case there are two middle terms (when number of terms is even), average of two middle terms is median. Doing so here we get `5, 5, 20, 20, 25, 30, 35` and as fourth term is middle term and it is `20`, median is `20`.

Mode is the term whose frequency is highest. Frequency of different terms in above example is given by `((5,2),(20,2),(25,1),(30,1),(35,1))`.

As highest frequency is for two terms, to identify mode, what one needs is making a grouping table (see an example at http://www.transtutors.com/homework-help/statistics/central-tendency-extended/grouping-method-examples.aspx). It is difficult to make such table here, but one could try and mode in this case will turn out to be `20`.

Range is the gap between smallest and largest data-point. As these are `5` and `35`, range is `35-5=30`.