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Measurement of Central Tendency, Mean, Median, Mode

Central tendency term is used for referring to the middle value or the typical values of a data. It is measured by using mean, median and mode. The calculation of each of these methods is different and involves differing ways of calculation and hence is used in accordance with the situation at hand.

Mean- it forms the most commonly used tool for the measurement of central tendency. While talking about the average, we refer to the mean only. The mean is calculated by summing up the items and then dividing them by the total number of the items of the set. The result thus obtained is termed as the arithmetic mean. When more weight is given to certain data points, the result obtained is called weighted arithmetic mean. Mean can be of various types

1. Arithmetic mean- it is the standard average and simply called as mean. It is obtained by calculating an arithmetic average of values or distributions and is represented as



2. Geometric mean- here the numbers are interpreted according to their product. For example rate of growth

It is represented by the equation


3. Harmonic mean-this type of averaging is useful for those sets which are determined in relation to some unit, for example distance per unit time


4. Truncated and interquartile mean- calculation of truncated mean requires discarding of some given parts of data at the top or bottom end of the table (normally an equal amount at each end) and then calculating the arithmetic mean of the remaining data.

The interquartile mean forms the specific example of truncated mean and is simply the arithmetic mean calculated after removal of the lowest and highest quarter of values. It can be expressed as



Median- Median is calculated by sorting the data set in the form of lowest to highest values and then taking the data points from the middle of the sequence. An equal number of points are obtained both above and below the median. We can obtain a median by calculating of a finite list of numbers by arranging all the observations form the lowest to the highest values and then picking the one found at the middle. The median of distributions can also be calculated by using their parameters. The median of a normal distribution having variance σ2 and mean μ is μ only. In actual practice, for a normal distribution all the three mean, mode and median are equal. A median can be determined both for ordinal as well as for ratio and interval data. In contrast to the mean ratio, the mean is not influenced by the outliners found at the extremities of the data set. This makes the median useful for calculation of extreme values which can greatly influence the mean and distort what is typical.

Mode- The mode is calculated by finding the most frequently value occurring in a data set or in a probability distribution. The mode is found most useful when dealing with categorical data but is also use in types of data which are ordinal, interval or ratio. In case of ratio and interval scales, the data is spread thinly and no data points have the same value. In these cases, the mode does not exist and if they do, they are not very meaningful.

Use of mean, median and mode- these three measures of central tendency can be best used by following the table below:

Measurement scale Best measure of the ‘middle’

Nominal/categorical Mode

Ordinal Median

Interval Symmetrical data-mean

Skewed data- median

Ratio Symmetrical data-mean

Skewed data-median

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