Measures of Central Tendency
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Measures of Central Tendency
Statistics is the very broad concept in the mathematics. In statistics there are three types of
measures of central tendency. They are mean, median and mode. Sometimes we called the
Measures of Central Tendency as the names of measures of central location.
The measures of central tendency are a single value that is used to explain the set of data by
obtaining the middle position that resides in the data set.
In other way we called the central tendency of measures as the names of summary statistics,
it is because; they summarized the information from the entire set of information.
The most likely measures of central tendency is mean that are also cal ed the average.
Measures of central tendency are the value that best explains the whole set of data or
information.
The measures of central tendency are the term that means finding the mean, median and
mode.
Let's take look on measures of central tendency one by one.
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Mean:  This is often cal ed as the average of the data set. It can be obtain by the following
way:
mean for grouped frequency distribution
I) Direct method:  mean = (fi * xi) / fi
where fi is the frequency and xi is the middle value of class interval.
i ) Assume mean method:  mean = A + fi * di / n
where di is the deviation and A is assumed mean.
Ii ) Step deviation method:  mean = A + h * (fi * ui ) / fi
Median :  Median is the central value in a given distribution. It divides the distribution into two
equal parts.
Median for grouped data :  median, Me = l + h * (n / 2  cf / f )
where l = lower limit of median class
h = width of median class
cf = cumulative frequency
N = fi
Mode :  Mode is the number that occurs most often in any distribution.
Mode for grouped data:  mode = Mo = x k + h f k  f k  1 / 2f k  f k  1  f k + 1
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where x k lower limit of the model class interval.
f k frequency of the model class.
f k  1 frequency of the class preceding the model class.
f k + 1 frequency of the class successding the model class
h = width of the class interval.
Let's take an example that will show the all measures of central tendency.
Example :  7, 6, 7, 9, 3, 2, 1
mean :  35 / 7 = 5
median :  first arrange the data into ascending order
1, 2, 3, 6, 7, 7. 9
median will be middle value so it is 6.
mode :  7 is the number that is occurring two times. So mode is 7.
Relationship between mean, median and mode is mode = 3(median)  2(mean)
So the measures of central tendency are a certain value representative of the whole data and
signifying its characteristics.
Note :  In a normal distribution the value of mean, median and mode is identical.
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