Why do we use averages?

- Averages are used to summarize a set of data points into a single representative value, providing a quick and easy way to understand the central tendency of a dataset.
- They help in comparing different datasets or analyzing trends over time by providing a common reference point.

Limitations of averages:

1. Sensitivity to outliers:
Averages can be heavily influenced by outliers, which are extreme values in the data set. These outliers can skew the average, making it an inaccurate representation of the majority of the data. For example, in a dataset of household incomes, a few extremely wealthy individuals can inflate the average income, giving a misleading impression of the overall distribution.

2. Disregard for variability:
Averages do not provide information about the variability or spread of data points within a dataset. Two datasets with the same average can have very different distributions. For instance, one dataset may have data points clustered closely around the average, while another dataset may have data points spread out widely. In such cases, relying solely on the average may overlook important nuances in the data.

In conclusion, while averages are useful for providing a general overview of data, it is important to be aware of their limitations. To gain a more comprehensive understanding of a dataset, it is advisable to complement averages with other statistical measures such as standard deviation, median, or quartiles.