The mean weight of salmon at a fishery is 15.8 pounds, with a standard deviation of 2.4 pounds. A researcher records the weight of the following salmon. 14.5lbs, 16.8lbs, 15lbs, 16.4lbs, and 15.9 lbs. Find µ, ơ, , and s
This problem wants you to show that you know the difference between a population and a sample. The fishery is the population, and the 5 measurements you have are the sample.
μ is the population mean, while x̅ is the sample mean
σ is the population standard deviation, while s is the sample standard deviation
The problem already gives you μ and σ
μ = 15.8 pounds
σ = 2.4 pounds
Now you have to calculate the mean and standard deviation for the sample.
x̅ = (14.5 + 16.8 +15 + 16.4 + 15.9) / 5
x̅ = 15.7 pounds
The equation to find the standard deviation of a sample is as follows:
s = √(∑(x-x̅)2 / (n-1))
So you have to add up (x-x̅)2 for each of the 5 terms. This gives you 3.67
Then you divide that by n - 1. n is the total number of terms, so 5 - 1 = 4
3.67/4 gives you 0.9175, then you take the square root of that, so s = 0.958 pounds
Here are your answers:
μ = 15.8 pounds
σ = 2.4 pounds
x̅ = 15.7 pounds
s = 0.958 pounds
