Theoretical distribution of sample means

Reference no: EM1380397

1. Consider the following distribution of grades in a class. Think of this as your population.

3	5
4	0 2 3 4 4 5
5	0 0 0 0 0 1 1 1 2 2 2 3 4 4 4 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 8
6	0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8
7	0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 5 5 5 5 6 6 6 7 7 7 7 8 8
8	0 0 0 0 0 1 1 2 2 6 7 8
9	0 0 1 4
10	0

a. Create the five-number summary and box plot for this data.

b. Calculate the mean, variance, and standard deviation for this data.

2. From this population, take a random sample of 10 observations.

a. Describe your sampling procedure. How did you ensure that your sample was a random one?

b. Give the frequency distribution for your sample.

c. What are the mean, variance, and standard deviation of the observations in your sample?

3. If you were to take sample after sample of size 10 from this population and calculated the sample mean for each of these samples

a. What would the distribution of sample means look like (what is the mean, variance, standard deviation, and shape for this distribution)?

b. Create an appropriate diagram to represent this distribution.

c. How does this distribution compare to the population distribution you would have been sampling from?

4. How does your sample compare to this theoretical distribution of sample means?

a. In other words, how probable was it to have observed a sample mean as far or further from the population mean than the one you did?

b. Create an appropriate diagram to represent this probability.

Reference no: EM1380397

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