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1. Mean, Median and Mode for ungrouped data example ( Enter your problem )

1. Formula & Examples

Formula
 1. Arithematic mean bar x = (sum x)/n 2. Median M = ((n+1)/2)^(th) value of observation in ascending order 3. Mode is that value of the observation which occurs maximum number of times.

Examples
1. Calculate Mean, Median, Mode from the following data
3,13,11,15,5,4,2,3,2

Solution:
Mean bar x = (sum x)/n

=(3 + 13 + 11 + 15 + 5 + 4 + 2 + 3 + 2)/9

=58/9

=6.4444

Median :
Observations in the ascending order are :
2, 2, 3, 3, 4, 5, 11, 13, 15

Here, n=9 is odd.

M= value of ((n+1)/2)^(th) observation

= value of ((9+1)/2)^(th) observation

= value of 5^(th) observation

=4

Mode :
In the given data, the observation 2,3 occurs maximum number of times (2)

:. Z = 2,3
2. Calculate Mean, Median, Mode from the following data
85,96,76,108,85,80,100,85,70,95

Solution:
Mean bar x = (sum x)/n

=(85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10

=880/10

=88

Median :
Observations in the ascending order are :
70, 76, 80, 85, 85, 85, 95, 96, 100, 108

Here, n=10 is even.

M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2

=(text{Value of } (10/2)^(th) text{ observation} + text{Value of } (10/2 + 1)^(th) text{ observation})/2

=(text{Value of }5^(th) text{ observation} + text{Value of }6^(th) text{ observation})/2

=(85 + 85)/2

=85

Mode :
In the given data, the observation 85 occurs maximum number of times (3)

:. Z = 85

This material is intended as a summary. Use your textbook for detail explanation.
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