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The following data are from a simple random sample.

$\begin{array}{llllll}{5} & {8} & {10} & {7} & {10} & {14}\end{array}$

a. What is the point estimate of the population mean?

b. What is the point estimate of the population standard deviation?

a. 9

b. 3.0984

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All right. So we're given that this is a sample of the population were supposed to find the point estimate for the mean and standard deviation. So let's start with a mean, so that's just gonna be we're gonna add these up. And then there's six data points, so this equals five full status. 13. 13% is 23 30 40 54 over six. This equals nine. All right now, to find our standard deviation. Ah, that's got to be similar to our standard deviation calculation for populations. So right, he's all out. All right. Now, if this r X and we find X minus mu, you are not mu it be ex bar. Actually, in this case, you refers to a population. All right, so five minus nine. Negative. Four negative. 11 negative. 215 All right, Now we square it. So that's 16 114 Uh, sorry, hon. 25. All right, we add these up. He's at up to 16 17 18 22 23 2025 23 is 48. Ah, we divide that bye and minus one. Since this is samples of 48 divide by six minus one because 48 over five, which is Ah, 9.6. Take the square root of that. That's approximately equal to 3.0 984 And there you have it.

University of California - Los Angeles