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1. Mean, Median and Mode for ungrouped data example
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 Formula & Examples

Other related methods
 Mean, Median and Mode
 Quartiles, Deciles and Percentiles
 Population Variance, Standard deviation and coefficient of variation
 Sample Variance, Standard deviation and coefficient of variation
 Population Skewness, Kurtosis
 Sample Skewness, Kurtosis
 Geometric mean, Harmonic mean
 Mean deviation, Quartile deviation, Decile deviation, Percentile deviation

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. Any bug, improvement, feedback then





