Harmonic Mean Formulas In Statistic

Harmonic Mean Formulas

Average harmonic is the average calculated by converting all data into fractions, of which the data value is used as the denominator and the numerator is 1, then all the fractions are summed and then used as the divisor of the amount of data.

Harmonic Mean Formulas in Statistic

H = n/(∑(1/x_i))

Information :

H = average harmonic value

n = amount of data

∑ = sigma notation

x_i = data

Example :

Please calculate the Harmonic mean of 3,5,6,6,7,10,12!

Answer :

n = 7

x_i = 3,5,6,6,7,10,12

H = n/(∑(1/x_i))

H = 7/((1/3)+(1/5)+(1/6)+(1/6)+(1/7)+(1/10)+(1/12))
H = 7/((4/12)+(1/5)+(2/12)+(2/12)+(1/7)+(1/10)+(1/12))

H = 7/(((4+2+2+1)/12)+(1/5)+(1/7)+(1/10))

H = 7/((9/12)+(1/5)+(1/7)+(1/10))

H = 7/((9/12)+(2/10)+(1/7)+(1/10))

H = 7/((9/12)+((2+1)/10)+(1/7))

H = 7/((9/12)+(3/10)+(1/7))

H = 7/((9/12)+(21/70)+(10/70))

H = 7/((9/12)+((21+10)/70))

H = 7/((9/12)+(31/70))

H = 7/((630/840)+(372/840))

H = 7/((630+372)/840)

H = 7/((1002)/840)

H = 7 x (840/1002)

H = 5880/1002

H = 5,87

So the harmonic average of 3,5,6,6,7,10,12 is 5,87

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