Theory:

Introduction:
In our daily life, we have read about information in the form of tables, graphs from books, newspapers, television, etc. The information can be temperatures in cities, number of people living, the weight of the students studying in a school, etc. These facts or information, which are in numerical form, is called data.
Data is a collection of facts or information which is used for a specific purpose.
The word "Data" is in the plural form and is derived from the Latin word "datum".
 
From these obtained data, we extract certain information. This extraction of information leads to a new concept in mathematics called "statistics".
Statistics is the branch of mathematics that deals with the collection, organising, analyzing and interpretation of data.
The word "Statistics" is derived from a Latin word "status" which means "a political state".
 
Let us recall the measures of central tendency that we have studied in earlier class.
Measures of Central Tendency:
The measures of central tendency are the value that tends to cluster around the middle value of the given set of data.
The following are the three measures of central tendency:
Mean
Mean is defined as the sum of all the observations divided by the total number of observations. It is usually denoted by x¯ (x bar).
Therefore, mean x¯= \(\frac{\text{Sum of all the observations}}{\text{Total number of observations}}\) =x1+x2+...+xnn
If the number of observations is very long, it is a bit difficult to write them. Hence, we use the Sigma notation \(\sum\) for summation.
 
That is, x¯=i=1nxin, where \(n\) is the total number of observations.
 
Also, in the case of ungrouped frequency distribution, the formula to find the mean is given by:
 
x¯=i=1nfixii=1nfi
Median
Median is defined as the middle value which exactly divides the given set of observations into two equal parts.
  1. If the number of observations (\(n\)) in the data set is odd, then the median can be determined using the formula, \((\frac{n+1}{2})^{th}\) observation.
  2. If the number of observations (\(n\)) in the data set is even, then the median is the mean of the values \((\frac{n}{2})^{th}\) and \((\frac{n}{2}+1)^{th}\) observations.
Mode
Mode is defined as the number which most frequently occurs in the given set of data. That is, the observation having the maximum number of frequency is called as mode.