Question

The three main measures of central tendency are the mean, median, and mode. Each of these could be impacted in different ways by an outlier that is distant from the other data points. Depending on the data set that you are describing, you might choose to use the mean, median, or mode to give a more accurate view of the data.  

Describe a situation where you might have an outlier in a data set. How will this outlier impact the result of each of these three measures of central tendency? Which one would you use to accurately describe the data set and why?

Answer 1

Solution:-

An outlier can affect the mean of a data set by skewing the results so that the mean is no longer representative of the data set. There are solutions to this problem.

Explanation:

As we have seen in data collections that are used to draw graphs or find means, modes and medians the data arrives in relatively closed order. In other words, each element of the data is closely related to the majority of the other data. If not, the data set may have information that is too scattered to be useful in any analysis.

In some data sets there may be a point or two that can be out of context with the bulk of the data. These are referred to as outliers, which are out of line with the normal data set. The outlier can push the mean of the data out of its usual position.
For example, the data set 3,4,5,6,7 has a mean of 5, found by dividing the sum of the data by the number of data elements:

If the 4 was mistakenly recorded as a 14, the 14 would be unusual for the data set and it would be an outlier.

And we can see the outlier has moved the mean of the data set.
To solve this problem the unusual data element can either be re-investigated and corrected, or removed from the data set with an explanation.

The former solution may bring back our original 4 after error checking is completed. The latter will return our mean closer to a representative evaluation of the data.