Statistics Formulas and Important Points

Mean Deviation=Sum of Deviations by Number of observations
The Deviation here means the difference of the observations from any of the central tendencies. But mostly we take the Deviation from Mean or Median but not from Mode.

Before we see more formulas we should see that the need for Mean Deviation is to get more accurate quantity to relate different quantities.

Here are the steps for finding Mean Deviation:
(a.) MD for Ungrouped Data

1. We derive the desired Central Tendencies.
2. We find the value of mod(x-a) for all x.
3. We use the formula for calculating MD:

(b.) MD for Grouped Data

Types of Grouped Data

1. Discrete Frequency Distribution
2. Continuous Frequency Distribution

•  Discrete Frequency Distribution

1. We find the desired Central Tendency by the formulas of basic Statistics.
2. We find the value of mod(x-a) for all frequency and observations.
3. We find the value of f×mod(x-a) for all frequency and observations.
4. We find MD by this formula:

For Central Tendency as Mean

For Median

• Continuous Frequency Distribution

1. We find the midpoint of the classes and take them as x
2. We will the follow the same steps as the Continuous Frequency Distribution.

In many books I have seen that there is one more method namely Shortcut method. This is nothing but the step deviation method by which the it becomes easy for finding Mean.

Mean Deviation for CF distribution for a as Median

This is a bit different now. Here Median can be find by this formula:

Rest all the formulas are the same.
I will post another post for Standard Deviation and Variance.