Descriptive Statistics

What is meant by Descriptive Statistics?
Descriptive statistics are generally used to describe the basic features of the data in a study. They
provide simple summaries about the sample and the measures.
In other words, descriptive statistics simply describes what is or what the data is coming to say.
Descriptive statistics are commonly used to simplify a large amount of data in the sensible and
the easier way.
How are they classified?
They can be broadly classified into two groups of categories such as measures of central
tendency and the measures of spread.
Measures of central tendency generally include mean, median and the mode.
Measures of spread include standard deviation, variance, skewness, minimum and maximum
Practical Application of Descriptive Statistics
One of the best practical examples of descriptive statistics is students grade point averages (
GPA) generally provided in the colleges. Because they generally take up data from different
exams, classes and grades. Students GPA generally reflect their academic performance.
Univariate Descriptive Statistics
This type of descriptive statistics generally focuses on one variable at a time.
Bivariate Descriptive Statistics
In this type, you can study the frequency and the variability of two variable at a time to know
whether they vary simultaneously.
Frequency of Distribution
In tables and graph, the frequency distribution of all possible values in the data set are generally
represented as values or the percentages.
Below is the example for the frequency distribution of an event,
Gender Participants
Man 100
Woman 200
No Records 0
The record generally shows more women participated in the event.

Measures of Central Tendency
As discussed earlier mean is the simplest method of measuring the averages.
Calculate the mean for the below-given data set.
Data Set = 24, 3, 0, 12, 3, 15
Total number of elements (N) = 6
Formula: Divide the sum of the values by N.
Ans: 57 / 6 = 9.5
Measures of Variability
The range is generally used to identify how far apart the extreme values are located.
Formula : Largest value in data set – The lowest value
Data Set = 24, 3, 0, 12, 3, 15
Ans: 24-0 = 24
Standard Deviation
It is generally used to identify how far each score lies from the mean.
Generally, there are six steps in finding the standard deviation.
Step 1: Find the mean.
Step 2: Subtract the mean value from each score to get the deviations from the mean.
Step 3: Square each deviated value.
Step 4: Find the sum of all the deviated value.
Step 5: Divide by N-1.
Step 6: As a next step find the square root of the value.
Data Set = 24, 3, 0, 12, 3, 15
Mean = 9.5
Ans = 421.5 / 5 = 84.3 = √84.3 = 9.18


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