Measures of Central Tendency & Dispersion in Data Analytics

Description

Measures of central tendency are statistics that tell us basic characterisitcs about a set of data. These are single number representatives of general characteristics of the group (not individual cases withing hte group), often called averages. Measures of central tendency are some of the most basic and useful statistical functions. They summarize a sample or population by a single typical value.

There are three measures of central tendency and each one plays a different role in determining where the center of the distribution or the average score lies. The commonly used measures of central tendency for numerical data are the mean , median and mode. In this course we will explain the calculation of Mean, Median and Mode

i) MEAN is the most commonly used measure of central tendency .The the mean is often referred to as the statistical average. The arithmetic mean is commonly called the average. When the word "mean" is used without a modifier, it can be assumed that it refers to the arithmetic mean. The mean is the sum of all the values divided by the number of  values. The formula is:
MEAN = ΣX/N
where N is the number of values.

ii) MEDIAN is a measure of central tendency determined as the least data value such that 50% of all values in the sample, or population, are less than or equal to it.

iii) The MODE is the most frequently occurring score in a distribution and is used as a measure of central tendency. The advantage of the mode as a measure of central tendency is that its meaning is obvious. Further, it is the only measure of central tendency that can be used with nominal data.
iv) If everything were the same, we would have no need of statistics. But, people's heights, ages, etc., do vary. We often need to measure the extent to which scores in a dataset differ from each other. Such a measure is called the dispersion of a distribution. Here we present various measures of dispersion that describe how scores within the distribution differ from the distribution's mean, mode and median. So in this course , we will also explain the calculation of Standard Deviation

The standard deviation is simply the square root of the variance. In some sense, taking the square root of the variance is opposite the squaring of the differences that we did when we calculated the variance. Variance and standard deviation of a population are designated by and , respectively. Variance and standard deviation of a sample are designated by s2 and s, respectively.

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