1. Given Mean- Find missing value

2. Arithmetic mean for ungrouped data
The arithmetic mean is the ratio of the sum of all the observations to the total
number of observations.
Arithmetic mean for ungrouped data
To calculate arithmetic mean for ungrouped data we use the following formula.
In Mathematics, the symbol in Greek letter Σ , is called Sigma
This notation is used to represent the summation Σx
With this symbol, the sum of x1, x2, x3, …… xn or simply as
Then we have
Note: Arithmetic mean is also known as Average or Mean.

3. More about notation: Σ

4. Example 1: The marks obtained by 10 students in a test are 15, 75, 33, 67, 76,
54, 39, 12, 78, 11. Find the arithmetic mean.
Solution:
Given:-Here, the number of observations, n = 10
To Find: Arithmetic mean (A.M.)
Ans:- Arithmetic mean is 46

5. Example 2: If the average of the values 9, 6, 7, 8, 5 and x is 8
Example 2: If the average of the values 9, 6, 7, 8, 5 and x is 8. Find the value of x.
Solution:
Given:-Here, the given values are 9, 6, 7, 8, 5 and average=8 and n = 6
To find: Value of x
By formula
ie., 35 + x = 48
x = 48 – 35 = 13
Ans:- x = 13

6. Example 3:-The average height of 10 students in a class was calculated as
166 cm. On verification it was found that one reading was wrongly recorded
as 160 cm instead of 150 cm. Find the correct mean height.
Solution
Given:-Here average = 166cm and n=10
The incorrect Σx = 1660
The correct Σ x = incorrect Σ x – the wrong value + correct value
= 1660 – = 1650
Hence, the correct A.M
Ans:- Correct mean height is 165cm

7. Try These
If the average of the values 18, 41, x , 36, 31, 24, 37, 35, 27,
36, is 31. Find the value of x.
The average height of 20 students in a class was calculated as
160 cm. On verification it was found that one reading was
wrongly recorded as 132 cm instead of 152 cm. Find the
correct mean height.