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# Mean Deviation for Grouped Data Calculator

Mean deviation in statistics is defined as the mean of the distances of each value from their mean. It is also referred to as mean absolute deviation. The data in a tabular form which indicates the frequency is known as a frequency distribution. Input the statistical grouped data (continuous / discrete frequency distribution) and the Mean Deviation for Grouped Data calculator will update you with the mean deviation (MAD) about median and mean.

## Calculate Mean Deviation of Frequency Distribution

Mean deviation in statistics is defined as the mean of the distances of each value from their mean. It is also referred to as mean absolute deviation. The data in a tabular form which indicates the frequency is known as a frequency distribution. Input the statistical grouped data (continuous / discrete frequency distribution) and the Mean Deviation for Grouped Data calculator will update you with the mean deviation (MAD) about median and mean.

#### Formula:

Mean = Multiplies of frequency data / Total value of frequency M.D (about mean) = ∑ (f |X−X̄|) / N Where, X = Number Data f = Frequency Data X̄ = Mean n = Number of Values M.D = Mean Deviation N = Sum of Frequency Data

### Example:

Find the MD of x=2,4,6,8 and f=3,4,5,6

#### Step 1 :

Find the mean of the data :
((2*3)+(4*4)+(6*5)+(8*6)) / (3+4+5+6) = 100/18 = 5.56

#### Step 2 :

Find the distance between each number data and mean.
Distance between 2 and 5.56 is 3.56
Distance between 4 and 5.56 is 1.56
Distance between 6 and 5.56 is 0.44
Distance between 8 and 5.56 is 2.44

#### Step 3 :

Muliply this each distance value with each frequency data:
(3.56*3)+(1.56*4)+(0.44*5)+(2.44*6) = 33.76

#### Step 4 :

Divide it by the sum of frequency data :
33.76 / (3+4+5+6) = 1.88
1.88 is the Mean Deviation.