Answer :
The point estimate of the population standard deviation is 7.688.
To calculate the point estimate of the population standard deviation, we use the formula for the sample standard deviation:
s = √((Σ(xi - x bar)^2) / (n - 1))
where s is the sample standard deviation, xi is each individual value in the sample, x bar is the sample mean, and n is the sample size.
Given the sample values 9, 13, 15, 15, 21, 24, we can calculate the sample mean:
mean = (9 + 13 + 15 + 15 + 21 + 24) / 6 = 97 / 6 ≈ 16.17
Next, we calculate the sum of squared differences between each value and the sample mean:
Σ(xi - x bar)^2 = (9 - 16.17)^2 + (13 - 16.17)^2 + (15 - 16.17)^2 + (15 - 16.17)^2 + (21 - 16.17)^2 + (24 - 16.17)^2 ≈ 178.67
Finally, we divide the sum of squared differences by (n - 1) and take the square root to obtain the sample standard deviation:
s = √(178.67 / (6 - 1)) ≈ 7.688
Therefore, the point estimate of the population standard deviation is approximately 7.688.
Learn more about standard deviation here:
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