Home > Statistical Methods calculators > Mean, Median and Mode for ungrouped data example


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
  5. Population Skewness, Kurtosis
  6. Sample Skewness, Kurtosis
  7. Geometric mean, Harmonic mean
  8. 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.
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