Measures of Dispersion, Median of Continues Frequcey Distribution, Mean Deviations from Median

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Median of Continues Frequcey Distribution:

Step 1:

Arrange the data in ascending order

Step 2:

Write cumulative frequencies of the observations

Step 3:

Identify the class whose cumulative frequency is just greater than .Call this class interval as median class.

Step 4:

Find median by the formula

Median

Where

Lower limit of the median class

Number of observations

Cumulative frequency of the class just preceding the median class

Frequency of the median class

Width of the median class

Example:

Find the median marks obtained by students from the following distribution:

Find the Median Marks Obtained
Find the median marks obtained

Marks

No. of Students

Solution:

The given intervals are already in ascending order. The following table has the row corresponding to the cumulative frequencies.

Find the Median Marks Obtained
Find the median marks obtained

Marks

No. of Students

Cumulative frequency

The class corresponding to the c.f. just greater than is .

Median class is

Where.

Median

Mean Deviations from Median:

We know that for observations in data the central tendency give us the values about which the data concentrate or cluster. It is also essential to know that how far all observation are, from a measure of central tendency.

In other words, in data it is required to know how dispersed the observations are from a given point (or a measure of central tendency). In most of the cases mean deviation from mean and median give us the desired dispersion or deviation of the observations.

Recall that mean deviation for data is defined as the mean of the absolute values of deviations from .

Recall that the deviation of an observation x from a fixed point is the difference .

So mean deviation about denoted by M.D is given by

M.D

Mathematically we can write

M.D

Like wise

M.D. (Mean)

And M.D.(Median M)

Algorithm to find mean deviation about mean/median:

Step 1:

Calculate the mean or median of the data

Step 2:

Find deviations of each observation xi from mean/median

Step 3:

Find the absolute values of the deviations.

Absolute values can be obtained by dropping the minus sign if it is there

Step 4:

Calculate the mean of the absolute values of the deviations. This mean will be the required Mean deviation.

Example:

Find mean deviation about median for the observation.

Solution:

In order to find median, arrange the given values in ascending order, so we have

,

Median th observation

observation

.

Deviations of the observation from median i.e. are

i.e. are

Absolute values of the deviations i.e. are

Now, M.D. (M)

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