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1. Mean, Median and Mode for ungrouped data example
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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`
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