Measures of Central Tendency

Mean
The mean of a given set of values is equal to the sum of all the values divided by the total number of values.

x = i = 1 n xi n

where, x = Mean
            ∑ = Summation sign
             n = Number of values
             xi = Values of x with i ranging from 1 to n.

           
average, mean, summation sign, sum of all frequencies, frequencies, measure of central tendency


Median
The value that lies in the very centre of a given set of values arranged in ascending or descending order, is called the median of the given data. The median is that value of the given number of observations, which divides it into exactly two parts.

If the number of given values is odd, median = [n + 1 2 ]th value, where n = number of given values.

If the number of given values is even, median = mean of ( 2 )th and (n+1  2 )th values, where n = number of given values.

Mode
The value that occurs the most number of times in a given set of values is called the mode of the given data or an observation with maximum frequency is known as mode.

Mean, Median and Mode together are called the measures of central tendencies of data. They are the representatives of the data. The central tendencies of a data depend on distribution of values and must be considered with other information for effective interpretation of data. Extreme values of a data affect the mean whereas median and the mode are not effected by the extreme values.

Summary

Mean
The mean of a given set of values is equal to the sum of all the values divided by the total number of values.

x = i = 1 n xi n

where, x = Mean
            ∑ = Summation sign
             n = Number of values
             xi = Values of x with i ranging from 1 to n.

           
average, mean, summation sign, sum of all frequencies, frequencies, measure of central tendency


Median
The value that lies in the very centre of a given set of values arranged in ascending or descending order, is called the median of the given data. The median is that value of the given number of observations, which divides it into exactly two parts.

If the number of given values is odd, median = [n + 1 2 ]th value, where n = number of given values.

If the number of given values is even, median = mean of ( 2 )th and (n+1  2 )th values, where n = number of given values.

Mode
The value that occurs the most number of times in a given set of values is called the mode of the given data or an observation with maximum frequency is known as mode.

Mean, Median and Mode together are called the measures of central tendencies of data. They are the representatives of the data. The central tendencies of a data depend on distribution of values and must be considered with other information for effective interpretation of data. Extreme values of a data affect the mean whereas median and the mode are not effected by the extreme values.

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