Statistics
This page provides an introduction to Statistics.
Overview
Statistics involves summarizing and describing the main features of a dataset, as well as drawing conclusions and making decisions based on data.
There are three types of data as below:
Ungrouped Data
A data where each observation is separate and distinct, with no grouping or classification.
For example, marks of students:
.
Discrete Frequency Data
A data where observations are grouped into distinct categories, with frequencies representing the number of times each category appears.
For example, student scores in a math test:
Continuous Frequency Data
A data where observations are grouped into continuous intervals or ranges, with frequencies representing the number of observations in each interval.
For example, Heights of people:
Measure of Central Tendency
Mean, Median & mode are measures of central tendency. It is single number representing the whole data.
Mean
Mean is an average value.
For Ungrouped data, mean formula is:
Where,
is observation,
is number of observations.
For discrete frequency data, mean formula is:
Where,
is observation group,
is frequency of observation group,
is number of observation groups.
For continuous frequency data, mean formula is:
Where,
is observation group,
is frequency of observation group,
is number of observation groups.
Median
Median is central value.
For ungrouped data, median is calculated as below:
First arrange the given data in ascending order or descending order.
- If total number of observations are odd then median is term.
- If total number of observations are even then median is arithematic mean of and terms.
For discrete frequency data, median is calculated as below:
- First arrange all observations in increasing order.
- Now calculate cummulative frequency ()
- Median is that observation () whose () is equal to or just greater than
For continuous frequency data, median is calculated as below:
- First arrange all observations in increasing order.
- Now calculate cummulative frequency ()
- Median is that observation () whose () is equal to or just greater than
Mode
Mode is most frequent value.
For ungrouped data, mode is:
An observation occuring maximum number of times.
For discrete frequency data, mode is:
An observation which has highest value of .
Where,
is value of observation group,
is frequency of observation group.
For continuous frequency data, mode formula is:
Where,
is lower limit of model class,
is frequency of the class above the model class,
is frequency of the model class,
is frequency of the class below the class,
is width of the class interval.
Model class is the class interval whose frequency is greatest.
If model class is the the last class internval, then value of will be .
Measure of Dispersion
It tells us if measure of central tendency is reliable or not
There are measures of dispersion:
- Mean deviation about , where can be mean, median or mode
- Variance(