Measures of Dispersion, Mean Deviation of Grouped Data from Median, Step to Find Mean Deviation from Median of a Continuous Frequency Distribution

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Mean Deviation of Grouped Data from Median

Recall that data presented in the following form are called grouped data

Discrete frequency distribution:

Discrete Frequency Distribution
Discrete frequency distribution

Observation:

Frequencies:

Continuous frequency distribution:

Continuous Frequency Distribution
Continuous frequency distribution

Observation:

Frequencies:

Example:

Find the mean deviation about median for the following data:

Find the Mean Deviation About Median
Find the mean deviation about median

Heights (in cm)

Number of Girls

Solution:

Let us first find median:

Let Us First Find Median
Let us first find median

Height (in cm)

Number of Girls (f)

Cumulative frequency (c.f)

lies in c.f. .

Median class is corresponding to the c.f. i.e.,

Now, Median

Where lower limit of the median class

sum of frequencies

c.f. of the class just preceding the median class

frequency of the median class

And width or class-size of the median class

Here,

To find mean deviation let us form the following table

Let Us First Find Median
Let us first find median

Height (in cm)

Number of Girls (f)

Mid value of the heights

Absolute Deviation

Mean Deviation (Median)

Step to Find Mean Deviation from Median of a Continuous Frequency Distribution:

Step 1:

Arrange the intervals in ascending order

Step 2:

Write cumulative frequencies

Step 3:

Identify the median class, as the class having c.f. just greater than , where is the total number of observations (i.e. sum of all frequencies)

Step 4:

Find the corresponding values for the median class and put in the formula:

Median

Where lower limit of the median class

Sum of frequencies

c.f. of the class just preceding the median class

Frequency of the median class

And width of the median class

Step 5:

Now form the table for following columns:

Now Form the Table for Following Columns
Now form the table for following columns

Given intervals

Frequencies

Mid-value

Absolute Deviation from

Step 6:

Now calculate M.D. (M)

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