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Home > Statistical Methods calculators > Box and Whisker Plots for ungrouped data example
Box and Whisker Plots Example-3 ( Enter your problem )
( Enter your problem )
  1. Formula & Example-1
  2. Example-2
  3. Example-3
 		Other related methods
  1. Mean, Median and Mode
  2. Quartile, Decile, Percentile, Octile, Quintile
  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
  9. Five number summary
  10. Box and Whisker Plots
  11. Construct an ungrouped frequency distribution table
  12. Construct a grouped frequency distribution table
  13. Maximum, Minimum
  14. Sum, Length
  15. Range, Mid Range
  16. Stem and leaf plot
  17. Ascending order, Descending order
2. Example-2
(Previous example)		11. Construct an ungrouped frequency distribution table
(Next method)

3. Example-3


3. Calculate Box and Whisker Plots from the following data
`3,13,11,15,5,4,2`

Solution:
Box and Whisker Plots :
`3,13,11,15,5,4,2`

Steps of Five-Number Summary

Step-1: Arrange the numbers in ascending order
`2,3,4,5,11,13,15`

Step-2: Find the minimum value
Minimum `=2` (the smallest number)

Step-3: Find the maximum value
Maximum `=15` (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.

`2,3,4,5,11,13,15`

`N=7` is odd, so median is the middle number at position 4

We have `5`

`:.` Median `=5`

Step-5: Place parentheses around the numbers above and below the median.
`{2,3,4},5,{11,13,15}`

Step-6: Find `Q_1` by finding the median for lower half of data(left of the median)

`2,3,4`

`N=3` is odd, so median is the middle number at position 2

We have `3`

`:.Q_1=3`

Step-7: Find `Q_3` by finding the median for upper half of data(right of the median)

`11,13,15`

`N=3` is odd, so median is the middle number at position 2

We have `13`

`:.Q_3=13`

Step-8: Summary found in the above steps.
Minimum `=2`

`Q_1=3`

Median `=5`

`Q_3=13`

Maximum `=15`



This material is intended as a summary. Use your textbook for detail explanation.
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2. Example-2
(Previous example)		11. Construct an ungrouped frequency distribution table
(Next method)


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