Statistics is a branch of mathematics that deals with the collection, review, and analysis of data. It is known for drawing the conclusions of data with the use of quantified models. Statistical analysis is a process of collecting and evaluating data and summarizing it into mathematical form.
Statistics can be defined as the study of the collection, analysis, interpretation, presentation, and organization of data. In simple words, it is a mathematical tool that is used to collect and summarize data.
Uncertainty and fluctuation in different fields and parameters can be determined only through statistical analysis. These uncertainties are determined by the probability that plays a very important role in statistics.
According to Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts or values in any department of inquiry placed in specific relation to each other”.
Data:
- Facts/figures, numerical or otherwise, collected for a definite purpose are called data.
- Data collected first-hand data:- Primary
- Secondary data: Data collected from a source that already had data stored
Frequency:
The number of times a particular instance occurs is called frequency in statistics.
Ungrouped data:
Ungrouped data is data in its original or raw form. The observations are not classified into groups.
Grouped data:
In grouped data, observations are organized in groups.
Class Interval:
- The size of the class into which a particular data is divided.
- Eg. divisions on a histogram or bar graph.
- Class width = upper class limit – lower class limit
Regular and Irregular class interval:
- Regular class interval: When the class intervals are equal or of the same sizes.
- Eg. 0-10, 10-20, 20-30….. 90-100
- Irregular class interval: When the class intervals are of varying sizes.
- Eg. 0-35, 35-45, 45-55, 55- 80, 80-90, 90-95, 95-100
Frequency table:
A frequency table or distribution shows the occurrence of a particular variable in a tabular form.
Sorting:
- Raw data needs to be sorted in order to carry out operations.-
- Sorting ⇒ ascending order or descending order
Ungrouped frequency table:
When the frequency of each class interval is not arranged or organised in any manner.
Grouped frequency table:
The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending.
Bar graphs:
Graphical representation of data using bars of equal width and equal spacing between them (on one axis). The height of the bar represents the frequency of the data.
Histograms:
- Like bar graphs, but for continuous class intervals.
- Area of each rectangle is ∝ Frequency of a variable and the width is equal to the class interval.
Frequency polygon:
If the midpoints of each rectangle in a histogram are joined by line segments, the figure formed will be a frequency polygon.
Midpoint of class interval:
The midpoint of the class interval is called a class mark
Class mark = (Upper limit + Lower limit)/2
Measures of Central Tendency
Average:
The average of a number of observations is the sum of the values of all the observations divided by the total number of observations.
Mean:
Mean for ungrouped frequency distribution \(\bar x= \frac{\sum x_if_i}{f_i}\)
Where \(f_i\) is the frequency of ith observation \(x_i\)
Mode:
- The most frequently occurring observation is called the mode.
- The class interval with the highest frequency is the modal class
Median:
- Value of the middlemost observation.
- If n(number of observations) is odd, Median =[(n+1)/2]th observation.
- If n is even, the Median is the mean or average of (n/2)th and [(n+1)/2]th observation.
