Page 2 - Lesson note-5-Ch 14 Statistics ( Measure of Central Tendency)

• Mode
Mean: The mean (or average) of a number of observations is the sum of the values of
all the observations divided by the total number of observations

It is denoted by the symbol ̅, read as ‘x bar’.

Mean for ungrouped data

Example 1.: Find the mean of 994, 996, 998, 1002 and 1000.
Given, No. of observations(n) = 5

we know, mean ( ) =

So, mean =

=
= 998
Hence, mean of the given numbers is 998

Example-2 : 5 people spend 10, 7, 13, 20 and 15 hours in doing social work in their
community..
Find the mean (or average) time in a week devoted by them for social work.

Solution:
To simplify our working of finding the mean, let us use a variable

this case, i can take the values from 1 to 5. So our first observation is , second
1
observation is , and so on till
2
5
Also, x1 = 10 means that the value of the first observation, denoted by , is 10.
1
Similarly, = 7, = 13, =20 and = 15.
4
2
3
5

Therefore, the Mean, Sum of all the observations
̅ = ------------------------------------= 13 hours
Total number of observations

For 30 observations, we use the Greek symbol

∑ (for the letter Sigma x) for summation.