Statistics is the science which is concerned with the collection, presentation and drawing of conclusions from numerical data. The numerical facts and observations collected are done with a specific purpose.
Scope of Statistics
i) Statistics are a sum total of observations. A single observation cannot form a statistic.
ii) Statistics are expressed quantitatively and not qualitatively.
Limitations of Statistics
i) Statistics laws are not exact. Actually they are true on averages only.
ii) Data collected for some specific purpose may not be suited for another purpose.
Presentation of data
i)Data obtained in the original form is called Raw or ungrouped data
ii)Data arranged in an ascending or descending fashion is called Arranged data
Variate
The quantity that may vary from observation to observation is called a variate
Classes
When we divide the values of the variate into convenient groups, we call them Classes
Frequency
The number of times the variate occurs is called the frequency of that variate
Frequency Table
A table showing the groups and their corresponding frequencies is called the frequency table
Let us take an example of the frequency table with continuous intervals
Class intervals
In this example there are 5 class intervals
I^{st} class interval = 020
II^{nd} class interval = 2040
III^{rd} class interval = 4060
IV^{th} class interval = 6080
v^{th} class interval = 80100
Upper limits and lower limits
0 is called the lower limit of the first class interval
20 is called the upper limit of the first class interval
Size of the class interval
Size of the class interval = upper limit of the class  lower limit of the same class
Class mark
The midvalue of a particular class is called the class mark of that class
Class mark = upper limit + lower limit /2
The class mark for the third class interval = 40 + 60 / 2 = 100/2 = 50
Range of the data
The difference between the highest variate and the lowest variate is called the range of the data.
Directions: Answer the following data. Also write at least 5 examples of your own of a set of data and find is range and frequency distribution.
