The mean is the average of all numbers and this is also called arithmetic mean. Mean can be calculated by adding all of the numbers in a set and then dividing the total count of numbers. For example, the mean of the numbers 2, 3, 7 is 4 therefore, 2+3+7=12 and 12 divided by 3 (there are three numbers) and the answer is 4.
To find the mean of a set of n number, x_{1}, x_{2}, x_{3}........x_{n} add the numbers in the set and divide the sum by n.
Mean (x) = \(\frac{x_1+x_2+x_3+......+x_n}{n}\)
= \(\frac{∑x}{n}\)
The greek letters ∑(called sigma) represents the sum of the numbers.
Example:
Find the mean of 2, 7 and 9
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
So, the mean is 6
Solution:
Given number
15, 13, 18, 16, 14, 17, 12
Here,
Sum of numbers (∑x) =15+13+18+16+14+17+12=105
Total numbers (n)=7
We have,
Mean(\(\overline{x}\)) =\(\frac{∑x}{n}\)
=\(\frac{105}{7}\)
=15
Solution:
The given data is 10, 18, 12, 30, 22, 14, 13
Sum of numbers (∑x)=10+18+12+30+22+14+13=119
Total numbers (n)=7
We have,
Mean(\(\overline{x}\))=\(\frac{∑x}{n}\)
=\(\frac{119}{7}\)
=17
Solution:
The given data is 84, 91, 88, 94, 91, 105, 98, 85
Sum of number (∑x) = 84+91+88+94+91+105+98+85 = 736
Number (n) = 8
Now,
Mean(\(\overline{x}\)) = \(\frac{∑x}{n}\)
= \(\frac{736}{8}\)
= 92
Solution:
The given data is 45, 35, 37, 32, 47, 38, 39, 36, 34, 37
Sum of number (∑x) = 45+35+37+3+47+38+39+36+34+37 = 380
Number (n) =10
Now,
Mean(\(\overline{x}\)) = \(\frac{∑x}{n}\)
= \(\frac{380}{10}\)
= 38
Solution:
The given data is 105, 108, 112, 106, 120, 108, 112, 110, 100
Sum of number (∑x) = 150+108+112+106+120+108+112+110+100 = 981
Number (n) = 9
Now,
Mean(\(\overline{x}\)) = \(\frac{∑x}{n}\)
= \(\frac{981}{9}\)
= 109
Solution:
Let, the third number be x.
Sum of number (∑x) = 50 + 60 + x = 110 + x
Number (n) = 3
Now,
Mean = \(\frac{∑x}{n}\)
or, 60 = \(\frac{110+x}{3}\)
or, 110 + x =180
or, x = 180 - 110
\(\therefore\) x = 70
Hence, the third number is 70.
Solution:
Let the third number be x.
Mean of 50, 60 and x = \(\frac{
Solution:
Let the third number be x.
Mean of 50, 60 and x = \(\frac{ 50 + 60 + x}{3}\)
So, 60 = \(\frac{110 + x}{3}\) ( mean= 60 )
Or, 110 + x = 180
Or, x = 180 - 110 = 70
Hence, the third number is 70.
Solution:
The given data is 10, 18, 12, 30, 22, 14, 13.
\(\sum\)x = 10 + 18 + 30 + 22 + 14 + 13 = 119
n = 7
We have, Mean =(\(\overline{x}\)) = \(\sum{\frac{x}{n}}\)
= \(\frac{119}{7}\)
= 17.
Solution:
Mean of 3, a + 2, 8, 12, 2a-1 and 6 =\(\frac{3 + a + 2 + 8 + 12 + 2a-1 + 6}{6}\)
7 = \(\frac{30 + 3a}{6}\)
Or, 30 + 3a = 42
Or, 3a = 42 - 30 = 12
Or, a = \(\frac{12}{3}\) = 4
Therefore, a = 4.
Find the mean of:
10, 18, 12, 30, 22, 14, 13
Find the arthmetic mean of the following data:
46, 24, 12, 25, 33
Find the mean of the following data:
15cm, 55cm, 32cm, 28cm, 40cm, 49cm.
Find the mean of the following data.
x | 5 | 10 | 15 | 20 | 25 | 30 |
f | 6 | 3 | 6 | 7 | 4 | 4 |
Find the mean of the following data.
x | 2 | 4 | 6 | 8 | 10 | 12 |
f | 12 | 8 | 9 | 10 | 6 | 5 |
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