A measure of central tendency is a single value that describes the way in which a set of data cluster around a central value. In other words, it is a way to describe the centre of a data set.
The three main measures of central tendency are:
- Mean
- Mode
- Median
Mean
The mean is a measure of central tendency that considers all of the values in the data set. One of the limitations of the mean as a measure of central tendency is, in order to calculate the mean, the data must be numerical. You cannot use the mean when you are working with nominal data, which is data on attributes or characteristics. For example, there cannot calculate the mean of defective loan applications.
The mean is also called the arithmetic centre of a distribution, stemming from the method to calculate the mean: the sum of all numbers in the data set, divided by how many numbers there are in the data set.
For example, the mean of 1, 2, 3, 4, 5, 6 would be calculated:
[1+2+3+4+5+6] / 6 = 3.5
The mean takes all numbers of a set of data into account, which could be deemed as a strength of the measure, but this also means that it is susceptible to skewing of the final calculated figure if the data features extreme values (or outliers).
For example, in a data set – 1, 2, 3, 4, 25 – the mean would be 7
Mode
The mode is a measure of central tendency that represents the most frequently observed value or range of values in a set of data. If there are two separate values that appear most often, the set is said to be “Bi-modal”.
The mode is useful when the set of data:
- has more than one segment (or multimodal)
- is badly skewed
- it is necessary to eliminate the effect of extreme values
Median
The median is the literal middle of the data set when arranged in order from smallest to largest. For an odd-sized sample, the median is equal to the literal middle number. To find the median an even-sized sample, add the two middle numbers and then divide the result by two.
The median of a distribution of data is determined as the 50th percentile point once the distribution has been defined.
For normal distributions, the median value occurs at or close to the mean of the distribution. This is also where the mode, or high point (most frequently occurring value), of the distribution, occurs.
Source: Sixsigmadsi.com
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