Measures of Central Tendency
Central tendency refers to the definition of a distribution of numbers by a particular central number. Generally speaking, it’s the most common number or most probable common number among a range of numbers.
If you’ve ever used the word ‘average’ in a sentence, eg On an average the temperature is 25 degrees here, you are more than familiar with the concept already.
Mean, Median and Mode are are the top 3 measures of central tendency. Some of the other measures are Geometric Mean, Harmonic Mean, etc.
Mean
The Average
The most common and frequently used terminology is the mean or average. It is defined as the sum total of units divided by the number of units.
Advantages
- Mean or average is understood universally
- Mean is easy to calculate
- It takes all values into consideration and doesn’t ignore any values.
Disadvantages
- Mean is prone to outliers. Since mean doesn’t ignore values, if there is a heavy concentration of high/low value numbers, the mean is affected. More on that later.
How To
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Mean = (2+2+4+5+7+9) / (6) = 5
Median
The Midpoint
A lesser used term in common language, but it has a huge significance in Statistics. Median is the middle / midpoint value in a sorted sequence. It divides the data 50:50.
Advantages
- Median is better at handling outliers as it doesn’t get affected by them
Disadvantages
- Median ignores all values and considers only one or two values.
How To
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Mean = (4 + 5) / 2 = 4.5
Mode
The Frequent
Simply put, mode is the most commonly occurring value.
Two modes = Bimodal ; Multiple modes = Multimodal
Advantages
- Mode can be used for categorical (non numerical) variables easily.
Disadvantages
- There can be more than one mode, or no mode at all.
- In statistics, mode can change the underlying nature of missing data and hence should be used less frequently or with a strong business reason.
How To
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Nomenclature
| Population | Sample |
|---|---|
| X = set of population elements | x = set of sample elements |
| N = population size | n = sample size |
| μ = population mean | x̄ = sample mean |
| σ = population std dev | s = sample std dev |
Population - our entire group of interest
Parameter - numeric summary about a population
Sample - subset of the population
Statistic - numeric summary about a sample