Why Divide by ? Let a population consist of the values 9 cigar...

Question

Why Divide by ? Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.)

a. Find the variance of the population {9 cigarettes, 10 cigarettes, 20 cigarettes}.

a. Find the variance of the population {9 cigarettes, 10 cigarettes, 20 cigarettes}.

Accepted Answer

Welcome back, everyone. Let a population consist of 35, and 12 cups of coffee consumed per day by 3 individuals. Find the variant of this population. A 12.45, B 14.90, C 16.25, and D, 18.75. So first of all, what we have to do is identify the mean of the population. We're going to take 35, and 12, we have to add them up, and we're going to divide by 3 because we have a sample of 3. We're going to get 6.67 rounded to 2 decimal places. Our next goal is to introduce a table, so we have x values, those are 35, and 12. And now in the next column we want to identify the difference between each X. And the mean value calculated. So for the first one, we're taking 3 minus 6.67. Which gives us -3.67. For the 2nd 15 minus 6.67, which is -1.67. And for the third one, we take 12 minus 6.67, which is 5.33. And now in the final column, we're going to square those differences. So we're squaring in 3.67. We get 13.49. Then we are squaring -1.67. This gives us 2.79. And finally, a less square 5.33, which gives us 28.41. Now to find variants, we simply want to write sigma squared, which represents variants. And then we want to add all of those differences squared, so we get 13.49. + 2.79. Plus 28.41. And what we have to do is basically divide this sum by the sample size, which is 3. We're going to get 14.90. That's our variance, and it corresponds to the choice B. Thank you for watching.

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Key Concepts

Population Variance

Mean Calculation

Sampling with Replacement

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