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Home > Statistical Methods calculators > Mean, Median and Mode for ungrouped data example
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Mean Example for ungrouped data
( Enter your problem )
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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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2. Mean Example
Measures of central tendency
There are 3 common measures of central tendency
1. Mean
2. Median
3. Mode
Mean :
The mean (or average) of number of observations is the sum of the values of observations divided by the total number of observations.
It is denoted by `bar x` and read as x bar.
So if `x_1,x_2,...,x_n` are n observations, then mean is
`bar x=(x_1+x_2+...+x_n)/n=(sum x)/n`
Here greek symbol `sum` (sigma) is used for summation.
1. Find the Mean of `3,13,11,15,5,4,2`
Solution:
Mean `bar x=(sum x)/n`
`=(3+13+11+15+5+4+2)/7`
`=53/7`
`=7.5714`
2. Find the Mean of `10,50,30,20,10,20,70,30`
Solution:
Mean `bar x=(sum x)/n`
`=(10+50+30+20+10+20+70+30)/8`
`=240/8`
`=30`
3. Find the Mean of `69,66,67,69,64,63,65,68,72`
Solution:
Mean `bar x=(sum x)/n`
`=(69+66+67+69+64+63+65+68+72)/9`
`=603/9`
`=67`
If values of observations are large, then to simplify calculation, Assume any number A and subtract it from all the observations.
Then mean is `bar x=A+(sum d_i)/n`, where `d_i=x_i-A`
4. Find the Mean of `69,66,67,69,64,63,65,68,72`
Solution:
| x | `d=x-A=x-65` |
| 69 | 4 |
| 66 | 1 | |
67 | 2 | |
69 |
4 | |
64 | -1 | |
63 | -2 | |
65 | 0 | |
68 | 3 |
| 72 | 7 |
| --- | --- | | `n=9` | `sum d=18` |
`bar x=A+(sum d_i)/n`
`=65+18/9`
`=65+2`
`=67`
This material is intended as a summary. Use your textbook for detail explanation.
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