For the following sample of n = 6 scores: 0, 11, 5, 10, 5, 5

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For the second one the numbers are 

For the following sample of n = 6 scores:
0, 11, 5, 10, 5, 5
Explain why the formula for sample variance is different from the formula for population variance. Why is it inappropriate to use the formula for
population variance in calculating the variance of a sample?
Variance is defined as the mean deviation, and, for a population, is computed as the sum of deviations divided by N. Without some
adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value.
Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of deviations divided by N. Without
some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value.
Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of squared deviations divided by N.
Without some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value.
Transcribed Image Text:Explain why the formula for sample variance is different from the formula for population variance. Why is it inappropriate to use the formula for population variance in calculating the variance of a sample? Variance is defined as the mean deviation, and, for a population, is computed as the sum of deviations divided by N. Without some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value. Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of deviations divided by N. Without some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value. Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of squared deviations divided by N. Without some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value.
On the basis of your plot, find the sample mean.
Mean = M =
Make an estimate of the standard deviation from the frequency distribution histogram. (Note: An estimate of the standard deviation can be made by
taking the average of the smallest and the largest deviations (from the mean) of the distribution)
For this distribution, the smallest distance from the mean is
and the largest distance is
The estimated standard
deviation =
Compute S, variance, and standard deviation for the sample.
SS =
Variance =
Standard deviation =
How well does your estimate compare with the actual value of s?
The calculated standard deviation differs slightly from the estimate.
The calculated standard deviation differs greatly from the estimate.
The calculated standard deviation is in excellent agreement with the estimate.
Transcribed Image Text:On the basis of your plot, find the sample mean. Mean = M = Make an estimate of the standard deviation from the frequency distribution histogram. (Note: An estimate of the standard deviation can be made by taking the average of the smallest and the largest deviations (from the mean) of the distribution) For this distribution, the smallest distance from the mean is and the largest distance is The estimated standard deviation = Compute S, variance, and standard deviation for the sample. SS = Variance = Standard deviation = How well does your estimate compare with the actual value of s? The calculated standard deviation differs slightly from the estimate. The calculated standard deviation differs greatly from the estimate. The calculated standard deviation is in excellent agreement with the estimate.
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