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Mean deviation and frequency distribution
A large data set is represented in a graphical or tabular form denoting the frequency of occurrence of each set of data. This observation is known as frequency distribution. For example, a class has how many cricketers, tennis players, and badminton players can be grouped into a frequency table to find out other relevant data. This grouping is known as grouped data and can be used to find out mean deviation.
Mean deviation of a grouped data
In a grouped data, the class intervals are arranged in such a way that they do not have any gaps, and each class has their own frequency.
Formula: - ∑ f | X-X| / ∑ f
where, f is the value of frequency
x is the mean, calculated as (sum of all the values/number of values) = ∑ f x / ∑ f
mid points are calculated as (lower limit + upper limit) / 2.
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X =∑ f x / ∑ f = 1350/50
X= 27
Mean Deviation=∑ f | X-X| / ∑ f
= 472/50
= 9.44
Hence, mean deviation is 9.44
Mean deviation of ungrouped data
In ungrouped data, some of the class intervals tend to be missing with irregular frequency distributions amongst them.
Example: - Find the mean deviation of the following ungrouped data.
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Solution
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We need to find the median first. Here total entries are 7, which is an odd number.
Therefore, median = item corresponding to the value of (n+1) /2
= 8/2 = 4th item = 8
Mean deviation = ∑ f |X-Me| / N = ∑ f | D| / N
= 15/7 = 2.14
Features of mean deviation
- The units of mean deviation are the same as that of the variables.
- They are rigidly defined.
- Their values depend upon each of the entered data.
- It is also known as absolute deviation because the values are absolute.
Advantages
- It gives a better result as all the values are taken into consideration for calculation.
- It is widely used in economics, businesses, commerce, and related fields
- It can be used to compare two or more series.
- Since the median is least affected by any of the terms, it gives a least affected result if extreme terms are changed.
Disadvantages
- It cannot be used if fractional data comes into being.
- Negative values cannot be taken into count.
- If samples increase, it becomes hectic to recalculate the whole data.
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