Mean Deviation Formula with Solved Examples

Mean Deviation Formula

The definition of mean deviation can be written as a statistical measure which is used to calculate the value of average deviation from the mean value of the data set which is given. The mean deviation of the given data values can easily be calculated.

Formula:

Below is the formula for the calculation of the mean deviation for any given data set.

[Σ |X – µ|]/N] = Mean Deviation

Here,

‘Σ’ is a symbol for the addition of values.

Each value in the data collection is represented by the letter ‘X’.

‘µ’ reflects the data set’s mean value

The number ‘N’ denotes the number of data values.

The absolute value is represented as | |, which ignores if it finds the “-” symbol.

Frequency Distribution Mean Deviation

We group the data and note the frequency distribution of each group to offer it in a more compressed format. The names given to these groups are class intervals.

Grouping of the data can possibly be done in the two ways:

• Discrete Frequency Distribution
• Continuous Frequency Distribution

Solved Examples

1. Calculate the standard deviation for the following data values: 7, 3, 6, 8, 4, 2.

The data values are 7, 3, 6, 8, 4, 2, and so on.

The process for the calculation of the mean deviation is already known to us.

To begin, calculate the mean of the data:

Mean, µ = ( 7+3+6+8+4+2)/6

µ = 30/6

µ = 5

The average value as a result is 5.

Subtract each mean from the data value, paying no attention to any minus symbols.

(Ignore”-”)

7 – 5 = 2

3 – 5 = 2

6 – 5 = 1

8 – 5 = 3

4 – 5 = 1

2 – 5 = 3

Now, the obtained data set is 2, 2, 1, 3, 1, 3.

Finally, find the average(mean) value for the data set that you have obtained

Therefore, the mean deviation is 

= (2+2+1+3+1+3) /6

= 12/6

= 2

As a result, the mean value for 7, 3, 6, 8, 4, 2 is 2.

1. Calculate the standard deviation for the following data values: 5, 8, 7, 3, 9, 4.

The data values are 5, 8, 7, 3, 9, 4, and so on.

The process for the calculation of the mean deviation is already known to us.

To begin, calculate the mean of the data:

Mean, µ = ( 5+8+7+3+9+4)/6

µ = 36/6

µ = 6

The average value as a result is 6.

Subtract each mean from the data value, paying no attention to any minus symbols.

(Ignore”-”)

5 – 6 = 1

8 – 6 = 2

7 – 6 = 1

3 – 6 = 3

9 – 6 = 3

4 – 6 = 2

Now, the obtained data set is 1, 2, 1, 3, 3, 2.

Finally, find the average(mean) value for the data set that you have obtained

Therefore, the mean deviation is 

= (1+2+1+3+3+2) /6

= 12/6

= 2

As a result, the mean value for 5, 8, 7, 3, 9, 4 is 2.