Populations

Populations

A population can be described using statistics. This involves identifying the correct information to use in terms of averages, spread and range.

The three averages: mode, median and mean, each have their own strengths and weaknesses.

A mode is not affected by extreme ranges, is easy to find, and can be used with non-numerical data. There may be instances when a single mode does not exist. A mode may not change if additional values are added; or it could change significantly.

A mean is affected by every value that is in the population, but can be distorted by extreme values.

A median may not change if additional values are added, and is not affected by extreme values.

The range indicates a spread of data across the population. An interquartile range indicates the spread of the central data, ignoring outliers.

Example 1

A company with five people pays salaries of £14,500, £15,200, £15,300, £17,500 and £28,000. Which average best describes the salaries paid by the company?

The mean would be distorted by the outlier (£28,000).

There is no mode.

The best average to use is therefore the median.

Answer: Median (£15,300)

Example 2

A company is going to use a five-star system for customers to leave feedback about their products, with 1 star being poor and 5 stars being excellent. Give one reason why using the modal number of stars would be a poor average to use.

As there is a limited range (1 to 5 stars) the mean would be a suitable average to use.

Answer: There may not be a modal value.