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Home > Statistical Methods calculators > Box and Whisker Plots for ungrouped data example
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Box and Whisker Plots Formula & Example-1
( Enter your problem )
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- Formula & Example-1
- Example-2
- Example-3
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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-1
Formula
Five number summary includes five values
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1. Minimum value
2. First quartile `Q_1`
3. Median `Q_2`
4. Third quartile `Q_3`
5. Maximum value
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Examples
1. Calculate Box and Whisker Plots from the following data `10,50,30,20,10,20,70,30`
Solution: Box and Whisker Plots : `10,50,30,20,10,20,70,30`
Steps of Five-Number Summary
Step-1: Arrange the numbers in ascending order `10,10,20,20,30,30,50,70`
Step-2: Find the minimum value Minimum `=10` (the smallest number)
Step-3: Find the maximum value Maximum `=70` (the largest number)
Step-4: Find the median The median is the middle number in a sorted data set and N is the total number of elements If N is odd then the median is a single middle number, and if N is even then the median is the average of the two middle numbers.
`10,10,20,20,30,30,50,70`
`N=8` is even, so median is the average of the two middle numbers at position 4 and 5
We have `(20+30)/2=25`
`:.` Median `=25`
Step-5: Place parentheses around the numbers above and below the median. `{10,10,20,20},{30,30,50,70}`
Step-6: Find `Q_1` by finding the median for lower half of data(left of the median)
`10,10,20,20`
`N=4` is even, so median is the average of the two middle numbers at position 2 and 3
We have `(10+20)/2=15`
`:.Q_1=15`
Step-7: Find `Q_3` by finding the median for upper half of data(right of the median)
`30,30,50,70`
`N=4` is even, so median is the average of the two middle numbers at position 2 and 3
We have `(30+50)/2=40`
`:.Q_3=40`
Step-8: Summary found in the above steps. Minimum `=10`
`Q_1=15`
Median `=25`
`Q_3=40`
Maximum `=70`
This material is intended as a summary. Use your textbook for detail explanation. Any bug, improvement, feedback then
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