In this part of lecture notes we will learn about MEAN, MODE and MEDIAN.
Mean
Mean in statistics is the same as average in Arithmetic. This is also called Arithmetic Mean.
Mean of Raw (or ungrouped) data:
The mean of n observations is given by the formula:
Here shows summation.
Similarly, we have:
Example:
The heights of plants in a garden are: .
Find the mean height.
Solution:
Sum of the given observations .
Number of observations .
Hence, the mean height is .
Mean Of Tabulated Data
Let the frequencies of n observations be respectively.
We define mean as:
Example:
The height of plants in a garden is given below:
Height (in cm)  58  60  62  64  66  68 
Number of plants  10  12  16  11  9  6 
Find the mean height of plant.
Solution:
We may prepare the table as shown below:
Height ( in cm ) 
No. of Plants  
58 
10  580 
60 
12  720 
62 
16  992 
64 
11 
704 
66 
9 
594 
68  6 
408 
Therefore,
Mean height
Mean of grouped Data
In a class interval, we take as the value of the value of the mark (average of the class range) and use the formula,
Example:
The following table shows the weight of persons in a group.
Weight (in kg)  4044  4448  4852  5256  5660 
Number of persons  8  12  9  16  5 
Solution:
We have
Weight ( in cm ) 
Frequency 
class mark 

4044 
8  42  42×8=336 
4448 
12  46  46×12=552 
4852 
9 
50 
50×9=450 
5256 
16 
64 
54×16=854 
5660  5  58 
58×5=290 
∴ Mean weight kg kg
Hence, the mean weight is kg.
Mode
The observation which occur maximum number of times is called the mode of the given data. In a tabulated data the observation with maximum frequency is the mode.
Example:
Given below is the data showing the size number of shoes sold by a shoe company in a day are . Find the mode of the data.
Solution:
In the given data, occurs maximum number of time
So, the mode of the given data .
Median
The median is the value separating the higher half of a data sample, from the lower half.
The basic advantage of the median in describing data compared to the mean (often simply described as the “average”) is that it is not skewed so much by extremely large or small values, and so it may give a better idea of a ‘typical’ value.
The first step is to arrange data in ascending or descending order of magnitudes, the value of the middle term is called the median of the data.
 When the number of observations is odd, then there will be only one midterm and this term is the median. This is
 When the number of observations is even, then there will be two middle terms. The average of these two middle terms will be the median of the data.
This is the mean of terms.
Example:
Find the median of the following data:
Solution:
Arranging in ascending order:
Number of terms .
So, and terms are the two middle terms.
Therefore,
Hence,