Statistics - Comparing Plots


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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.

Comparing plots

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 −

Comparing plots

${OVS = 13 - 6 \\[7pt] \ = 7 \\[7pt] \ DBM = 10 -3 \\[7pt] \ = 4 }$

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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