Mean in statistics and mathematics is the most used tool of measures of central tendency. There are different types of mean – arithmetic mean, geometric mean, and harmonic mean. And in this article we have discussed mean, mean formula, types of mean, and their formulas.
Mean and its calculation:
The mean is simply an average of the given data set. To calculate the mean, first, the sum of all the values in the given set of data is computed and then the sum is divided with that total number of values in the data set. Given below, is the formula of mean when ungrouped data is given:
Mean = Sum of all observations in a data set / Total number of observations in the data set
The formula of the mean can be represented symbolically as:
x̄ = ∑x/n
where,
x̄ = calculated mean
∑ = observations that are to be added
x = all observations in the given data set
n = total number of values in the given data set
The mean for the ungrouped data can be calculated using three methods:
1. Direct method: This method uses the following formula to calculate the mean:
Mean = ∑xifi / ∑fi
2. Assumed Mean method: This method uses the following formula to calculate the mean:
Mean = A +∑fidi / ∑fi
3. Step-deviation method: This method uses the following formula to calculate the mean:
Mean = A + h ∑fiui ∑fi
Different types of mean and their calculation:
There are three types of mean in statistics and mathematics:
Arithmetic Mean
Arithmetic mean is calculated by dividing all add-up values given in the data set by the total number of values in the same data set. Following given is the formula to calculate the arithmetic mean:
Arithmetic Mean = ∑x/n
For example, to calculate the arithmetic mean of 4, 6, 2, 8, 5, first all the given numbers are added (4 + 6 + 2 + 8 + 5 = 25) and then the sum is divided by total numbers (5).
Here,
sum of all values (∑x) = 25
total values (n) = 5
Arithmetic mean = 25 / 5 = 5
Geometric Mean
Geometric mean of the values given in the data set is calculated by multiplying all the given values and then square rooting the obtained multiplied value. Following given is the formula to calculate the geometric mean:
Geometric Mean = nx1x2x3……..xn
For example, to calculate the geometric mean of 3, 5, 6, and 4, first the given numbers are multiplied (3 × 5 × 6 × 4 = 360), then the square root of computed multiplied value (360) is calculated.
Geometric Mean = 360 = 18.97
Harmonic Mean
Harmonic Mean = usage of harmonic mean is to average ratios. The harmonic mean of the value given in the data set is calculated by dividing the total number of values in the set of data by the calculated sum of the reciprocals of each value given in the same data set. Following given is the formula to calculate harmonic mean:
Harmonic mean = n1x1+1x2+1x3+……1xn
For example, to calculate the harmonic mean of 4, 2, 5, and 3, first, observe the total number of given values (4), then add the reciprocals of the given values ( 14 + 12 + 15 + 13 = 7760) and finally, divide the total numbers by the computed sum of reciprocal values.
Harmonic Mean = 47760 = 5.45
Bottom Line
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