For the above data calculate the mean, variance and standard deviation.

Question

Twelfth fish caught had a mass of 2.3kg. summary data for the mass in kg of the 12 fish are follows. Sigma x = 21.4. Sigma x ^2= 40.54

Answer 1

Given: set X of xn samples where n = 12

total mass M_x = 2.3

sigma (σ_x) = 21.4

sigma squared ( σ_x²) = 40.54

The above were the given conditions. Here are standard definitions

definition for mean of a set of n samples = ∑x_n. /n.

definition for standard deviation σ = √ V. (V = Variance)

There is a major problem here in that two incompatible values are given. σ is stated to be 21.4 and σ² is stated to be 40.54. BUT σ · σ (sigma times sigma) actually equals 457.96 , not the stated 40.54.

The question as stated contains critical errors. The values stated can not exist. No answer is possible which refers to variance or standard deviation. Mean can be calculated as 191.7 g but this appears to be totally incompatible with the stated variance which when normality is assumed, would mean more than 49% of the population of fish caught would have negative weights.

Please go back to your original problem description and data and re-format your question.