Arithmetic mean definition:
Arithmetic mean of two numbers: The arithmetic mean of two numbers is the number that comes in exactly the middle of the two numbers. Consider the arithmetic mean example: Find the arithmetic mean of 2 and 4. The answer here would be 3, because 3 is the same distance from both 2 and 4. The method for finding arithmetic mean of two numbers is very simple, we simply add the two numbers and divide by 2. In other words, half the sum of the numbers equals the arithmetic mean. Symbolically it can be written like this:
A = (a+b)/2, where a and b are the numbers of which we are to find the arithmetic mean and A is the arithmetic mean.
Arithmetic mean of n numbers: If there are many numbers, then the arithmetic mean would be the sum of all the numbers divided by the number of numbers. Therefore if there are 4 numbers, a,b,c and d then their arithmetic mean would be = (a+b+c+d)/4. Similarly for n number it would be:
A.M. = [∑xi]/n, where i = 1,2,3,…. n and xi are each of the numbers x1,x2,x3,…. Xn.
The above arithmetic mean equation holds good for any number of numbers, provided that n is a finite number. Arithmetic mean symbol used in statistics is μ or x ̅.
Uses of arithmetic mean:
Arithmetic mean is a very useful measure of central tendency in statistics. For a large data, the easiest measure of central tendency is the arithmetic mean. Arithmetic mean is also useful in case of grouped data. In case of grouped data, the arithmetic mean is same as the weighted average. Consider the following example:
Example: The following table represents the marks of students in a class of 25. Find the average marks of the class.
Solution:
For a grouped frequency distribution the formula for arithmetic mean is:
x ̅ = ∑xifi / ∑fi. So lets add a third column for ∑xifi for the above data.
x ̅ = 164/25 = 6.56
Arithmetic mean of two numbers: The arithmetic mean of two numbers is the number that comes in exactly the middle of the two numbers. Consider the arithmetic mean example: Find the arithmetic mean of 2 and 4. The answer here would be 3, because 3 is the same distance from both 2 and 4. The method for finding arithmetic mean of two numbers is very simple, we simply add the two numbers and divide by 2. In other words, half the sum of the numbers equals the arithmetic mean. Symbolically it can be written like this:
A = (a+b)/2, where a and b are the numbers of which we are to find the arithmetic mean and A is the arithmetic mean.
Arithmetic mean of n numbers: If there are many numbers, then the arithmetic mean would be the sum of all the numbers divided by the number of numbers. Therefore if there are 4 numbers, a,b,c and d then their arithmetic mean would be = (a+b+c+d)/4. Similarly for n number it would be:
A.M. = [∑xi]/n, where i = 1,2,3,…. n and xi are each of the numbers x1,x2,x3,…. Xn.
The above arithmetic mean equation holds good for any number of numbers, provided that n is a finite number. Arithmetic mean symbol used in statistics is μ or x ̅.
Uses of arithmetic mean:
Arithmetic mean is a very useful measure of central tendency in statistics. For a large data, the easiest measure of central tendency is the arithmetic mean. Arithmetic mean is also useful in case of grouped data. In case of grouped data, the arithmetic mean is same as the weighted average. Consider the following example:
Example: The following table represents the marks of students in a class of 25. Find the average marks of the class.
Marks (xi) (max marks = 10)
|
Number of students (fi)
|
2
|
1
|
3
|
1
|
4
|
2
|
5
|
3
|
6
|
3
|
7
|
6
|
8
|
6
|
9
|
2
|
10
|
1
|
Solution:
For a grouped frequency distribution the formula for arithmetic mean is:
x ̅ = ∑xifi / ∑fi. So lets add a third column for ∑xifi for the above data.
xi
|
fi
|
Xi*fi
|
2
|
1
|
2
|
3
|
1
|
3
|
4
|
2
|
8
|
5
|
3
|
15
|
6
|
3
|
18
|
7
|
6
|
42
|
8
|
6
|
48
|
9
|
2
|
18
|
10
|
1
|
10
|
∑
|
25
|
164
|
x ̅ = 164/25 = 6.56
No comments:
Post a Comment