# Statistics - Means Difference

The mean difference (more correctly, 'difference in means') is a standard statistic that measures the absolute difference between the mean value in two groups in a clinical trial. It estimates the amount by which the experimental intervention changes the outcome on average compared with the control.

## Formula

${Mean\ Difference= \frac{\sum x_1}{n} - \frac{\sum x_2}{n}}$

Where −

• ${x_1}$ = Mean of group one

• ${x_2}$ = Mean of group two

• ${n}$ = Sample size

### Example

Problem Statement:

There are 2 dance groups whose data is listed below. Find the mean difference between these dance groups.

 Group 1 Group 2 3 9 5 7 5 3 4 4

Solution:

${ \sum x_1 = 3 + 9 + 5 + 7 = 24 \\[7pt] \sum x_2 = 5 + 3 + 4 + 4 = 16 \\[7pt] M_1 = \frac{\sum x_1}{n} = \frac{24}{4} = 6 \\[7pt] M_2 = \frac{\sum x_2}{n} = \frac{16}{4} = 4 \\[7pt] Mean Difference = 6-4 = 2 }$

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