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Descriptive statistics gives us the summary and description of the features of the data under study. In order to present the data in a meaningful manner, we make use of Descriptive Statistics.
Descriptive statistics only tell us about the basic descriptive and summary of the data. Inferential Statistics, on the other hand, helps us to perform deeper analysis and draw conclusions that descriptive statistics are unable to do. Inferential statistic allows us to collect a sample and that sample is used to draw conclusions about the population.
Suppose we have the following Box-plot:
The above box-plot contains the median, first quartile, third quartile, minimum, and the maximum values. It tells us about the five-number summary of the data. In other words, it gives us description of the data.
The Measures of Descriptive Statistics is broadly divided into two groups - Measures of Central Tendency and Measures of Dispersion or Variability.
The following are the various measures of Central Tendency:
Let x1, x2,....., xnbe n observations. Then Mean denoted byx- is given by:
Case 1: For odd number of observations:
In the above figure, we see 18 is the middlemost value and hence it is the median for the odd set of numbers.
Case 2: For even number of observations:
In the above figure, we see 18 and 20 are the middlemost values of the even set of numbers. For the median, we calculate the mean of 18 and 20 that is
15 is the most frequent value and hence the mode of the above data.
The following are the various measures of dispersion:
The standard deviation denoted by o is defined as:
Interquartile range (IQR) = Q3-Q1
Thus, Descriptive Statistics gives us a general idea and summary of the data. It helps us to represent the data in a meaningful manner.
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