Note on Mean

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Example

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 = \(\frac{ 50 + 60 + x}{3}\)

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%
  • Find the mean of:

    10, 18, 12, 30, 22, 14, 13

     

    2
    20
    18
    17
  • Find the arthmetic mean of the following data:

    46, 24, 12, 25, 33

     28
     30
     25
     33
  • Find the mean of the following data:

     15cm, 55cm, 32cm, 28cm, 40cm, 49cm.

     33cm
     36.5cm
     30cm
     35cm
  • The mean of 8, 7, 9, 10, 12, a and 14 is 12, find the value of a.

    28
    26
    25
    24
  • Find the mean of the following data.6, 12, 9, 3, 22, 21

    12
    12.17
    15
    11
  • The mean of 3, x+2, 8, 12, 2x-1 and 6 is 7, find the value ofa.

    7
    6
    5
    4
  • The arthematic mean of four numbers is 42. If three of the numbers are 34, 38 and 46, find the fourth number.

    55
    50
    48
    45
  • The arthematic mean of five numbers is 50. If three of the numbers are 40, 45 and 75, find the mean of fourth and fifth numbers.

    48
    55
    45
    58
  • The mean of 3, a+2, 8, 12, 2a - 1 and 6 is 7, find the value of a.

    5
    7
    4
    3
  • The arthematic mean of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?

    75
    55
    70
    87
  • Find the mean from the following data. 4, 12, 13, 21, 12, 12, 10

    12
    10
    17
    15
  • Find the mean from th efollowing data. 15, 13, 18, 16, 14, 17, 12

    12
    15
    22
    17
  • Find the mean. 45, 35, 37, 32, 47, 38, 39, 36, 34, 37

    45
    36
    39
    38
  •  Find the mean of the following data.

      x  5  10  15  20  25  30
      f  6  3  6  7  4  4

     

     17
     12
     18
     15
  •  Find the mean of the following data.

      x   2   4   6   8   10   12
      f   12   8   9   10   6   5

     

     6.2
     7
     5.5
     6.5
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