Mean
Arithmetic Means
If the total sum observation is divided by a total number of observations, then it is called arithmetic mean. It is denoted by \(\overline{X}\) (Read as Xbar)
∴ Arithmetic Mean = \(\frac{Total\;sum\;of\;observation}{Total\;no.\;of\;observation}\)
For example,
Arithmetic mean of 1, 3, 7, 11, & 13
= \(\frac{1+3+7+11+13}{5}\)
= \(\frac{35}{5}\)
= 7
 Calculation of Mean for individual series
The mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.
If x_{1}, x_{2}, x_{3}, …………..x_{n} are be n variants value of variable a. Then arithmetic mean is denoted by
\(\overline{X}\) = \(\frac{x_1+ x_2+ x_3+ …………..x_n}{n}\) = \(\frac{∑X}{n}\)
Where ∑X = sum of n observation or items
n = no. of observations or items.
X = variable.  Calculation of Mean for discrete series
Mean for discrete series can be calculated by Mean \(\overline{X} = \frac{sum\;of\;the\;product\;of\;f\;and\;x}{sum\;of\;f}\)
= \(\frac{∑fx}{N}\)  Calculation of Mean for continuous series
For calculating mean in continuous series the following formulae is used:
\(\overline{X}\) = \(\frac{∑fx}{N}\) where, F = Frequency and m = midvalue.
 If the total sum observation is divided by total number of observations, then it is called arithmetic mean. It is denoted by \(\overline{X}\).
 The mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.

Marie has the following data:
2, 2, k, 14, 3
If the mean is 6, which number could k be?
1
9
5
6

Find mean.
9, 5, 7, 0, 7, 4, 4, 1, 7, 6
5
7
6
2

Find mean.
4, 8, 12, 16 , 20
12
16
5
8

Find mean.
6, 16, 20, 30, 36
25.02
21.6
46
20

What is the mean?
7, 0, 6, 6, 5, 6, 3, 1, 6, 8
6
2
1
3

Brinda tallied the number of times her favourite new song played on 8 radio stations this week. She tallied:
4 plays 5 plays 6 plays 8 plays 4 plays 7 plays 9 plays 5 plays What was the mean number of plays?
5
4
9
6

Find the value of k from the given data whose mean is 23.
10, 17, 19, k, 27 , 29, 33
41
26
25
12

Find the value of x from the given data whose mean is 8.
x, 7, 9, 8, 10, 12
4
2
56
12

Find the value of P from the given data whose mean is 34.
20, 24, 32, 40, P & 52
21
25
36
45

Find the value of x from the given data whose mean is 22.
x, x+4, x+8, x+12, x+16
15
20
25
14

Find the value of Q if the mean of 10, 22, 12, 8, 14, Q and 20 is 16.
20
18
26
12

Find the mean.
90, 50, 70, 30, 20, 10
45
60
80
55

The age (in years) of 15 students are as follows. Calculate their average age.
12, 13, 11, 12, 15 , 14 , 11, 12 , 12, 11, 13, 12, 11
12
13
12.33
14

The mean of 5, 7, 9, x and 15 is 10, find x.
14
15
16
12

The mean of 3, 7, 10, 15 and x is 12, find x
25
5
15
20

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