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Showing posts with label mode. Show all posts

Tuesday, October 9

Introduction to Statistics Examples


The study of data is called Statistics.  Collections of observation of an individual or a number of individuals is called data.

Collection of data:  There are two types of data namely Primary data and Secondary data.

Primary Data:  The data which is collected by the investigator with a definite object for his own purpose is called Primary Data.

Secondary Data:  The data which is collected by someone other than the investigator is called Secondary Data.

Statistics Examples: Measures of Central Tendency

Measures of Central Tendency:

A numerical value which represents approximately the entire statistical data is called Measures of Central Tendency of the given data.

The different ways of measuring central tendency of a statistical data are

Mean,  Median  and  Mode.

Statistics Examples: Mean

Mean :

The mean of a set of data is the same as finding average.

Mean = `(Sum of all observations )/(Total Number of Observations)`

`Mean of ungrouped data:`

` Mean = ``sum_(i = 1)^n` `f_(i)` `x_(i)`
                ------------------------------
                   `sum_(i = 1)^n` `f_(i)`

Ex :

Find the mean of the following data:

x f
25 25
35 20
45 15
55 15
75 10

Solution:

Construct another tabe:

x f fx
25 25 625
35 20 700
45 15 675
55 15 825
75 10 750
85 3575

` Mean = ``sum_(i = 1)^n` `f_(i)` `x_(i)`
                 ---------------------------------
                    `sum_(i = 1)^n` `f_(i)`

Mean =  `sum`fx /  `sum`f
=3575 / 85
=42.06

Statistics Examples: Median

Median for Raw data:

Arrange the set of datas in ascending or descending order.  The middle most value is the Median.

Rule 1:  If n is odd, the median = `(n + 1)/(2)` th term

Rule 2 :  If n is even, there are two middle terms ie `(n)/(2)`  th term and  `(n)/(2)` + 1 th term.

In this case , the arithmetic mean of these two terms is the median.

Median =     `(n)/(2)`  th term  +  `(n)/(2)` + 1 th term
                        ----------------------------------------
                                                  2

Ex 1:
Find the median of 6, 7, 2, 5 and 10

Sol:
Arrange the given datas in ascending or descending order:
2, 5, 6, 7, 10
Here n= 5 ( odd number)
Median =  `(n + 1)/(2)` th term =  `(5 + 1)/(2)` th term
=   `(6)/(2)` th term
=  3 rd term
=   6

Ex 2:
Find the median of : 6, 11, 15, 7, 19, 8, 4, 10

Sol :
Arrange the given datas in ascending or descending order:
4, 6, 7, 8, 10, 11, 15, 19
Here n = 8 ( even)
Median =    `(n)/(2)`  th term  +  `(n)/(2)` + 1 th term
                     ----------------------------------------
                                              2

Median  =   `(8)/(2)`  th term  +  `(8)/(2)` + 1 th term
                     ----------------------------------------
                                             2

Median  =   `(4th term + 5th term)/(2)`
 = ``(8 + 10)/(2)`
= 18 / 2
= 9

Statistics Examples : Mode

Mode:  Mode is the repeated value of the given data

Ex: Find the mode for the given data:  34, 56, 21, 56, 71, 98, 22, 56

Sol: In the given data 56 is repeated thrice.  So the mode is 56.
Mode for tabulated data:

Number  7 8 9 10 11 12 13 14 15
Frequency 3 7 11 14 13 17 12 8 6

Sol:  Since the frequency of number 12 is maximum
Mode = 12