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Home > Statistical Methods calculators > Mean, Median and Mode for ungrouped data example
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Mean, Median and Mode for ungrouped data Formula & Example
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- Formula & Example
- Mean Example
- Median Example
- Mode Example
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Other related methods
- Mean, Median and Mode
- Quartile, Decile, Percentile, Octile, Quintile
- 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
- Five number summary
- Box and Whisker Plots
- Construct an ungrouped frequency distribution table
- Construct a grouped frequency distribution table
- Maximum, Minimum
- Sum, Length
- Range, Mid Range
- Stem and leaf plot
- Ascending order, Descending order
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1. Formula & Example
Formula
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1. Arithematic mean `bar x = (sum x)/n`
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2. Median M = `((n+1)/2)^(th)` value of observation in ascending order
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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`
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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