Suppose that my 3 siblings and I are the following heights, in inches.
72 69 77 66
a. Calculate and report the range of this distribution.
b. Calculate and report the variance of this distribution.
c. Tell me how you calculated this.
d. Calculate and report the standard deviation of this distribution.
e. Write a sentence or two in which you tell me, using your own words, what a standard deviation is (in general, not this particular standard deviation).
f. Wrap words around the mean and standard deviation of this distribution. What do they tell you about the distribution of scores?
g. Pretend that this distribution of scores represents a sample rather than a population. Calculate and report the standard deviation.
h. Explain why the standard deviation you reported for question 1d differs from the standard deviation you reported for question 1g.
i. Suppose that in the population of birds that live in the trees on a university campus, the average number of feathers is 1000 with a standard deviation of 200. Wrap words around that standard deviation. What does it tell you, exactly?

Question

Quizplus · Accepted Answer

The Answer is a. 77 - 66 = 11
b. 16.5
c. I took each score, subtracted the mean from it, and squared it:
(72-71)² = 1, (69-71)² = 4, (77-71)² = 36, (66-71)² = 25
Then you add these all together: 1+4+36+25 = 66
Then you divide this sum by the number of cases in the population: 66/4 = 16.5
d. The square root of the variance is the standard deviation. So, sq. root of 16.5 = 4.06.
e. It is the average difference between the mean and the scores in the distribution.
f. The average height of my siblings and I is 71 inches with a standard deviation of 4.06 inches, so the average difference between out individual heights and the mean height is 4.06 inches.
g.This is a population because my siblings and I are all of the members of a group (my parents' children). So when calculating the s.d., I divided the variance by N, which was 4. But if this had been a sample, I would have divided by n - 1, which is 3. So 66/3 = 22, and the square root of 22 is 4.69. So had this been a sample, the s.d. would have been 4.69.
h. Because for a sample we us n - 1 in the denominator, not N.
i. The average difference between the mean of the population and the individual scores in the population is 200 birds.

Suppose That My 3 Siblings and I Are the Following