Groups of population can be compared using box and whisker plots. Overall visible spread and difference between median is used to draw conclusion that there tends to be a difference between two groups or not.

## Case 2: Formula

${P = \frac{DBM}{OVS} \times 100 }$

Where −

- ${P}$ = percentage difference
- ${DBM}$ = Difference Between Medians.
- ${OVS}$ = Overall Visible Spread.

## Rules

- For a sample size of 30 if this percentage is greater than 33% there tends to be a difference between two groups.
- For a sample size of 100 if this percentage is greater than 20% there tends to be a difference between two groups.
- For a sample size of 1000 if this percentage is greater than 10% there tends to be a difference between two groups.

## Example

## Problem Statement:

Describe the difference between following sets of data.

Sr. No. | Name | Set A | Set B |
---|---|---|---|

1 | Max | 12 | 15 |

2 | UQ | 10 | 13 |

3 | Median | 7 | 10 |

4 | LQ | 6 | 9 |

5 | Min | 5 | 6 |

## Solution:

Consider the following diagram:

${OVS = 13 – 6 \\[7pt]

\ = 7 \\[7pt]

\ DBM = 10 -3 \\[7pt]

\ = 4 }$

Apply the formula

${P = \frac{DBM}{OVS} \times 100 \\[7pt]

\ = \frac{4}{7} \times 100 \\[7pt]

\ = 57.14 }$

As percentage is over 33% thus there is difference between Set A and Set B. It is likely that Set B is greater than Set A.

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