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.

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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`

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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`

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

`:. Z = 2,3`

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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`

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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`

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

`:. Z = 85`

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