# Statistics: Measures of Central Tendency

Whenever any metric of interest (e.g. share price of a stock, the height of an individual, score of a student, delay in the arrival of a flight, etc.) is measured, a fairly large number of observations in the sample tend to centre around a single value. This value can be considered as a single representative value of the desired metric for the sample. As these values give the ‘location’ of a ‘central’ value of the sample, they are called more commonly “Measures of Central Tendency” of the sample.

There are different statistics to measure the central tendency of any data. In this module, we will cover the most important measures of Central Tendency — Mean, Median, Mode, Percentile and Quartile

# Mean

Mean is the most common measure of central tendency. Mean can be defined for all ratio-scale and interval-scale data. To calculate the mean, simply add all of your numbers together. Next, divide the sum by however many numbers you added. The result is your *mean *or average score.

# Median

Median is the middle number of any data series which has been sorted in ascending (i.e. lowest to highest) or descending (i.e. highest to lowest) order. If the series is odd, then the median is exactly the middle number. However, if the series is even, then it is the average of the middle two numbers. Median is defined for ordinal data too, along with interval-scale or ratio-scale data.

# Mode

In statistics, the mode in a list of numbers refers to the integers that occur most frequently. Unlike the median and mean, the mode is about the frequency of occurrence. There can be more than one mode or no mode at all; it all depends on the data set itself.

# Percentiles

In statistics, percentiles are used to understand and interpret data. The *n*th percentile of a set of data is the value at which *n* per cent of the data is below it. In everyday life, percentiles are used to understand values such as test scores, health indicators, and other measurements. An 18-year-old male who is only five and a half feet tall, on the other hand, is in the 16th percentile for his height, meaning only 16 per cent of males his age are the same height or shorter.

percentiles should not be confused with percentages. The latter is used to express fractions of a whole, while percentiles are the values below which a certain percentage of the data in a data set is found. In practical terms, there is a significant difference between the two.

# Quartiles

A quartile is a statistical term that describes a division of observations into four defined intervals based on the values of the data and how they compare to the entire set of observations. Quartiles are the values that divide a list of numerical data into three quarters. The middle part of the three quarters measures the central point of distribution and shows the data which are near to the central point.

The lower part of the quarters indicates just half the information set which comes under the median and the upper part shows the remaining half, which falls over the median. In all, the quartiles depict the distribution or dispersion of the data set