Question

Calculate the arithmetic and harmonic means for each of the following sets of numbers:

a. 10, 20, 60

b. 10, 10, 50, 50

c. 10, 20, 50, 80, 90

Please show ALL work and equations used.

Answer 1

Here the answer of your Question with steps below,

Arithmetic mean : The arithmetic mean is defined as the sum of all observation divided by no. of observation. In other words the mean is nearest value of all observations.

Harmonic mean : is the reciprocal of the arithmetic mean of the reciprocals. In other words, it is the number of observations, divided by the sum of reciprocals of the observations. This is also is one of several kinds of average and it is appropriate for situations when the average of rates is desired.

a. 10, 20, 60

The arithmetic mean : Solution :
Mean Value = 5 + 8 + 12 + 15 + 20/5
= 60/5
Mean = 12

The Harmonic mean :

Data set = 10, 20, 60
Total number of observation= 3

Formula :

Steps :
Harmonic mean =31/10 + 1/20 + 1/60
=30.1 + 0.05 + 0.0167
=30.1667
Harmonic mean = 18

b.10,10,50,50

The Arithmetic mean : Input Data :
Data set = 10, 10, 50, 50
Total number of elements = 4

Formula :


Solution :
Mean Value = 10 + 10 + 50 + 50/4
= 120/4
Mean = 30

The Harmonic mean : Input Data :
Data set = 10, 10, 50, 50
Total number of observations = 4

Formula :


Solution :
Harmonic mean =41/10 + 1/10 + 1/50 + 1/50
=40.1 + 0.1 + 0.02 + 0.02
=40.24
Harmonic mean = 16.6667

c. 10,20,50,80,90

The arithmetic mean :

Data set = 10, 20, 50, 80, 90
Total number of elements = 5

Objective :
Find what is mean value for given input data?

Formula :
formula to calculate sample or population mean

Solution :
Mean Value = 10 + 20 + 50 + 80 + 90/5
= 250/5
Mean = 50

The Harmonic mean : Data set = 10, 20, 50, 80, 90
Total number of obs = 5

Formula :


Solution :
Harmonic mean =51/10 + 1/20 + 1/50 + 1/80 + 1/90
=50.1 + 0.05 + 0.02 + 0.0125 + 0.0111
=50.1936
Harmonic mean = 25.825

Here is the detailed calculation of your Question.

Hope you understood then RATE POSITIVE ?. In case of any queries please feel free to ask in comment box.

Thank you.