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Statistics is the branch of mathematics which deals with data collection tabulation of data, analysis of data and drawing conclusion for such purpose
Eg ;The marks obtained by 10 students in a unit test in mathematics are given below.The total marks were 20 and the pass marks were 10.
6 , 11, 14, 14, 15, 17, 17, 17, 18, 20 .
From the data , we can classify the data as follows
Marks Obtained | Telly marks | No of Students |
6 | / | 1 |
11 | / | 1 |
14 | // | 2 |
15 | / | 1 |
17 | /// | 3 |
18 | / | 1 |
20 | / | 1 |
Total | 10 |
From the collected in a class of 10 students, we have classified the data as shown above .Marks which are here are variables so it is called variate . The number which is repeated is called frequency .The total number of frequency is the total number of students .
Here frequency is denoted by f and its sum by Σƒ is also denoted by N .The variate is usually denoted by X .
Usually, data can separate into three parts :
Individual series ;It is usually listed in dates which are collected in small scale .They are also known as raw data . eg;The amount of money brought by 6students is
eg;The amount of money brought by 6students of school for their tiffin.
Rs 4, Rs 5, Rs 7, Rs 10, Rs 11, These kind of data are less in number and need not be arranged in a table .
Here, the number of data is denoted by n .
In the above example , n = 5 .
Discrete series ;Tose series which are formed by discrete values are called discrete series .
The marks obtained by 10 students in a class test is given below;
Marks | 6 | 10 | 12 | 14 | 15 | 18 | 20 |
No of students | 1 | 2 | 1 | 1 | 3 | 1 | 1 |
Here, marks denote the variate values and the number of students denotes the frequencies .
Continuous Series ;Those series which can be represented by a continuous variable is called continuous series . we mostly use this kind of data to insert large scale of data.
eg;
The marks obtained by 100 students in an examination is given below :
Marks | 0 -10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
Numbers of students | 10 | 30 | 20 | 15 | 25 |
In this series, the data lie within the group .Its Interval or groups are called class intervals.The end points of a class interval are called limits .
eg; 0 - 10 0 is called lower limit.
Here,the average of data is very important .Mean or average of data which single represents the whole set of data This represents the central data .Here, a percentage of students is the average marks of all the marks he or she gets in their exam.
Mean of data is calculated by adding all the data togeather and dividing them by the total number of data .
Mathematically,
Mean =\(\frac{Sum\ of \ the\ data}{Total\ no\ of \ data}\)
=\(\frac{∑χ}{N}\)
Where x is the variate values
∑χ is the sum of all variates
n is a total number of dates
Note :
∑ is read as sigma or summation .
In discrete series
In case of discrete series or ungrouped repeated data , we find mean by
Mean (\(\overline{X}\)) = \(\frac{∑ƒχ}{N}\)
Where,X is the variate
ƒ is the frequency
ƒx is the product of ƒ and x
∑ƒχ is the sum of ƒχ.
N is the total number of frequency.
Those data which divides the given set of data into two equal halves is called median . It is denoted by Md . Here we need to arrange our data in either ascending or descending order for calculating the median .
Median ( Md ) = value of \(\frac{(n+1)^{th}}{2}\)
Where , n = total no of items .
Solution :
Here, the data are 3 ,7 , 9 , 10 , 15
Which are already in ascending order .
So , number of data ( n ) = 5
Now , Median ( Md ) = value of \(\frac{( n + 1 )^{th}}{2}\)item
=value of \(\frac{( 5 + 1 )^{th}}{2}\)item
=value of \(\frac{6}{2}^{th}\)item
∴ Median ( Md ) = 9 .
Solution :
The dates are 18, 11, 14, p, 17,
Number of dates (n) = 5
∑x = 18 + 11 + 14 + p + 17
=60 + p
Now, we know , mean \(\overline{X}\)= 14
So, mean \(\overline{X}\) = \(\frac{∑X}{n}\)
or, 14 = \(\frac{60 + p}{5}\)
or, 70=60 + p
or, 70-60 = p
or, 10= p
∴ The value of p is 10 .
Solution ,
Here the datas are 1, 2, 3, 4, 5.
number of datas ( n ) = 5
∑x = 1 + 2+3+4+5
=15
Now, mean \(\overline{(X)}\)=\(\frac{∑X}{n}\)
=\(\frac{15}{5}\)
=3
______ is the branch of mathematics which deals with data.
Mean is also known as _____ .
Average is calculated as the sum of _____ and _____ .
Mean is denoted by ______ .
In discrete series (overline{X}) =_____ and_____ .
If ∑ƒx = 80 and (overline{X})= 8 , n =_____
The average of 2 and 4 is _____
Medain divides the set of data into _____ parts .
Median in individual series is calculated as_____
If ∑ƒx = 80 and (overline{X}) = 8 , n =_____
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