# Statistics - Trimmed Mean

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Trimmed Mean a method of averaging that removes a small percentage of the largest and smallest values before calculating the mean.

The Trimmed Mean can be calculated using the following formula.

## Formula

$\mu = \frac{\sum {X_i}}{n}$

Where −

• $\sum {X_i}$ = Sum of your Trimmed Set.

• ${n}$ = Total Numbers in Trimmed set.

• ${\mu}$ = Trimmed Mean.

### Example

Problem Statement:

Figure out the 20% trimmed mean for the number set {8, 3, 7, 1, 3, and 9}

 Items 14 36 45 70 105
Trimmed Mean Percent = $\frac{20}{100} = 0.2$; Sample Size=6

Give us a chance to first ascertain the estimation of Trimmed check (g), where g alludes to number of qualities to be trimmed from the given arrangement.

g = Floor (Trimmed Mean Percent x Sample Size) g = Floor (0.2 x 6) g  = Floor (1.2)
Trimmed check (g) = 1


Record the given arrangement of numbers {8, 3, 7, 1, 3, 9} in rising request, = 1, 3, 3,7,8,9

As the trimmed tally is 1, we ought to expel one number from the earliest starting point and end. Along these lines, we uproot first number (1) and last number (9) from the above arrangement of numbers, = 3, 3, 7, 8.Now Trimmed mean can be computed as:

$\mu = \frac{\sum {X_i}}{n} \\[7pt] \, = \frac{Sum\ of\ your\ Trimmed\ Set}{Total\ Numbers\ in\ Trimmed\ set} \\[7pt] \, = \frac{(3 + 3 + 7 + 8)}{4} \, = \frac{21}{4} \\[7pt] \, = {5.25}$

The Trimmed Mean of the given numbers is 5.25.

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