 # Descriptive Statistics

Statistics is the science of collecting data and analyzing them to infer proportions (sample) that are representative of the population. In other words, statistics is interpreting data in order to make predictions for the population.
Branches of Statistics:
There are two branches of Statistics.

• DESCRIPTIVE STATISTICS : Descriptive Statistics is a statistics or a measure that describes the data.
• INFERENTIAL STATISTICS : Using a random sample of data taken from a population to describe and make inferences about the population is called Inferential Statistics.
Descriptive Statistics is summarizing the data at hand through certain numbers like mean, median etc. so as to make the understanding of the data easier. It does not involve any generalization or inference beyond what is available. This means that the descriptive statistics are just the representation of the data (sample) available and not based on any theory of probability.

## Commonly Used Measures

1. Measures of Central Tendency
2. Measures of Dispersion (or Variability)

## Measures of Central Tendency

A Measure of Central Tendency is a one number summary of the data that typically describes the center of the data. These one number summary is of three types.

1. Mean : Mean is defined as the ratio of the sum of all the observations in the data to the total number of observations. This is also known as Average. Thus mean is a number around which the entire data set is spread.
2. Median : Median is the point which divides the entire data into two equal halves. One-half of the data is less than the median, and the other half is greater than the same. Median is calculated by first arranging the data in either ascending or descending order.
• If the number of observations are odd, median is given by the middle observation in the sorted form.
• If the number of observations are even, median is given by the mean of the two middle observation in the sorted form.

An important point to note that the order of the data (ascending or descending) does not effect the median.

3. Mode : Mode is the number which has the maximum frequency in the entire data set, or in other words,mode is the number that appears the maximum number of times. A data can have one or more than one mode.

• If there is only one number that appears maximum number of times, the data has one mode, and is called Uni-modal.
• If there are two numbers that appear maximum number of times, the data has two modes, and is called Bi-modal.
• If there are more than two numbers that appear maximum number of times, the data has more than two modes, and is called Multi-modal.