Question

How are measures of central tendency affected by outliers?

Answer 1

Hint: We first describe the concept of central tendency and the use of outliner and its effects on it. We take an example to understand the concept better. The smaller the sample size of the dataset, the more an outlier has the potential to affect the central tendency.

Complete step-by-step answer:
In statistics, outliers are causing the mean to increase, but if we have outliers to the left of the graph these outliers are dragging down the mean. This causes a conflict because the mean no longer provides a good representation of the data, alternatively we would much rather use the median. The median on the other hand is less likely to be affected by outliers.
Sample mean can be expressed as $\bar{x}={\displaystyle \frac{\sum x_i}{n}}$ for inputs as $x_i,i=1(1)n$.
But while the mean is a useful and easy to calculate, it does have one drawback: It can be affected by outliers. In particular, the smaller the dataset, the more that an outlier could affect the mean.
Outliner skews the results so that the mean is no longer representative of the data set.
We take an example: Ten students take an exam and receive the following scores of $0,88,90,92,94,95,95,96,97,99$.
The mean is $$\bar{x}={\displaystyle \frac{0+88+90+92+94+95+95+96+97+99}{10}}={\displaystyle \frac{846}{10}}=84.6$$.
Now if we remove 0 from the sample means the means becomes 94.
The one unusually low score of one student drags the mean down for the entire dataset.

Note: When an outlier is present it can affect the shape of the graph, if we have outliers to the right of the graph. An outlier can affect the mean by being unusually small or unusually large. The mean is non-resistant. That means, it's affected by outliers. More specifically, the mean will want to move towards the outlier.