## Note on Mean

• Note
• Things to remember
• Exercise
• Quiz

#### Mean

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, x1, x2, x3........xn 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

• The mean is the  sum divided by the count.
• The mean is the average of the numbers.
• The mean isn't a value from thye original list.
.

### Very Short Questions

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.

0%

17
20
18
2

33
28
30
25

36.5cm
35cm
30cm
33cm

26
24
28
25

11
12
15
12.17

5
7
4
6

48
55
45
50

45
58
48
55

5
4
7
3

87
75
70
55

12
10
15
17

17
22
12
15

36
39
45
38

17
15
18
12

6.5
7
5.5
6.2