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