Mean, Median and Mode - Introduction to Statistics - Lecture Slides, Slides of Economic statistics

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Intro to Stats for Muslims

Unit 02: Descriptive Statistics

Lecture 3: Representing & Benchmarking: Mean, Median and Mode

Reduce Data to ONE number

 Data Summary REVEALS central aspect, and CONCEALS diversity.  It is necessary only because we don’t have sufficient mental capacity to look at whole data set all at once.  Many different ways of summarizing data.  Using one number in place of whole data ALWAYS conceals more than it reveals.

Mean or Average

 Pool all resources. Divide them equally among all. Everyone’s share is the mean or average.  Representative number IF there is near equality in the population.  Not representative if there is substantial inequality, or diversity.

Median: middle of the data set

 Sort data set: Middle value is median.  If even number of data, then average of the two middle values.  Illustrate by sorting, do both manually and in EXCEL.

MODE: The most common value

 Look at heights data: which is the most common measure for height?  HIES data set on Family Size. What is the most common family size?

Bimodal Distributions: Mixtures

 When two populations are mixed in data set, bimodal distrbutions result.  GDP Data is bimodal. Plot histogram in EXCEL and show. Explain that there are rich countries and poor countries – two groups.  Artificial Heights Data is bimodal. Plot already included. Display.

Failures of Mean

 Mean does not represent or benchmark in bimodal distributions.  Same is true of median.  Illustrate by examples with GNP data set.  Illustrate by example in lecture.

Modes

 Modes are useful to identify cases of mixtures.  Modes work as representatives in bimodal or multimodal distributions. In this case both mean and median fail.