Prove the relation between arithmetic, geometric and harmonic mean for the following data Classes 0-95 100-195 200-295 300-395 400-495 500-595 600-695 700-795 800-895 Frequency 102 192 230 300 139 233 204 185 178
Prove the relation between arithmetic, geometric and harmonic mean for the following data Classes 0-95 100-195 200-295 300-395 400-495 500-595 600-695 700-795 800-895 Frequency 102 192 230 300 139 233 204 185 178
Prove the relation between arithmetic, geometric and harmonic mean for the following data Classes 0-95 100-195 200-295 300-395 400-495 500-595 600-695 700-795 800-895 Frequency 102 192 230 300 139 233 204 185 178
Prove the relation between arithmetic, geometric and harmonic mean for the following data
Classes
0-95
100-195
200-295
300-395
400-495
500-595
600-695
700-795
800-895
Frequency
102
192
230
300
139
233
204
185
178
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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