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1. Mean, Median and Mode for ungrouped data example ( Enter your problem )
  1. Formula & Examples
Other related methods
  1. Mean, Median and Mode
  2. Quartiles, Deciles and Percentiles
  3. Population Variance, Standard deviation and coefficient of variation
  4. Sample Variance, Standard deviation and coefficient of variation

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 follwing 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 follwing 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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