arithmetic, geometric, and harmonic mean The following data set is taken from 11

Question

arithmetic, geometric, and harmonic mean

The following data set is taken from 11 samples from the same aquifer. These are measured values for the hydraulic conductivity. 4. K =[4.3 x 10-4, 6.1 x10-3, 2.5 x 10-5, 1.2 x 10-4, 1.0 x10-6, 7.1 x 10-3, 9.1x10-6, 2.2 x 10-3, 4.2 x 10-5,8.7 x10-4, 3.5x 10-5] m/s As you can see, the hydraulic conductivity varies from sample to sample. Perform the following statistical analyses a. b. c. Calculate the arithmetic mean of the data set. Calculate the geometric mean of the data set. Calculate the harmonic mean of the data set.

Explanation / Answer

Addition

K

0.00043

0.0061

0.000025

0.00012

0.000001

0.0071

0.0000091

0.0022

0.000042

0.00087

0.000035

0.0169321

Arithmetic mean: The sum of all of the numbers in a list divided by the number of items in that list

= 0.016932/11 = 0.001539

geometric mean is defined as “the nth root of the product of n numbers.”

= 11 [(0.00043)( 0.0061)…( 0.000035)]

= 11 (1.43047 * 10^-42)

= 1.57*10^-4 = 0.000157

K

0.00043

0.0061

0.000025

0.00012

0.000001

0.0071

0.0000091

0.0022

0.000042

0.00087

0.000035

1/K

2325.58

163.93

40000

8333.33

1000000

140.85

109890.11

454.55

23809.52

1149.43

28571.43

harmonic mean is the reciprocal of the arithmetic mean of the reciprocals

= n / [(1/x1)+(1/x2)..+(1/xn)]

= 11/ [(1/0.00043)+(1/0.0061)+..+(1/0.000035)]

= 11/ 1214838.7

= 9.056*10^-6

= 0.000009056

Addition

K

0.00043

0.0061

0.000025

0.00012

0.000001

0.0071

0.0000091

0.0022

0.000042

0.00087

0.000035

0.0169321

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