# If you have two groups. The fi

If you have two groups. The first group got somesimilar numbers but over a wider range of numbers. The second groupgot less similar numbers but the numbers were in a closer range.Which group had the much more precise results? The group withsimilar numbers but over a wider range or the group with only onematch but all numbers were very close together?

Some Limitations of Range

Range is quite auseful indication of how spread out the data is, but it has someserious limitations. This is because sometimes data can haveoutliers that are widely off the other data points. In these cases,the range might not give a true indication of the spread ofdata.

For example, in ourprevious case, consider a small baby rat added to the data set thatweighs only 50 grams. Now the range is computed as 480-50 = 430grams, which looks like a false indication of the dispersion ofdata.

This limitation ofrange is to be expected primarily because range is computed takingonly two data points into consideration. Thus it cannot give a verygood estimate of how the overall data behaves.

Practical Utility of Range

In a lot of cases,however, data is closely clustered and if the number ofobservations is very large, then it can give a good sense of datadistribution. For example, consider a huge survey of the IQ levelsof university students consisting of 10,000 students from differentbackgrounds. In this case, the range can be a useful tool tomeasure the dispersion of IQ values among university students.

Sometimes, we definerange in such a way so as to eliminate the outliers and extremepoints in the data set. For example, the inter-quartile range instatistics is defined as the difference between the third and firstquartiles. You can immediately see how this new definition of rangeis more robust than the previous one. Here the outliers will notmatter and this definition takes the whole distribution of datainto consideration and not just the maximum and minimum values.

It should be pointedout that in spite of several limitations, the range can be a usefulindication for many cases. As a student of statistics you shouldunderstand what kinds of data are best suited to be defined basedon range. If there are too many outliers, it may not be a goodidea. But range gives a quick and easy to estimate indication aboutthe spread of data.

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