The annual incomes of the five vice presidents of TMV Industries are: $125,000; $128,000; $122,000; $133,000; and $140,000. Consider this a population.

What is the population variance? The standard deviation? What is the range? What is the arithmetic mean income?
The annual incomes of officers of another firm similar to TMV Industries were also studied. The mean was $129,000 and the standard deviation $8,612. Compare the means and dispersions in the two firms.
Sample Variance The formula for the population mean is ยต = SX/N. We just changed the symbols for the sample mean that is X = SX/n. Unfortunately, the conversion from the population variance to the sample variance is not as direct. It requires a change in the denominator. Instead of substituting n (number in the sample) for N (number in the population), the denominator is n 1. Thus the formula for the sample variance is:
2
2 E(X - X)
S = --------------------
N - 1
s2 is the sample variance.
X is the value of each observation in the sample.
X is the mean of the sample.
n is the number of observations in the sample.

Exercise 2
Determine the mean and the standard deviation of the following frequency distribution.
Class Frequency
0 up to 5 2
5 up to 10 7
10 up to 15 12
15 up to 20 6
20 up to 25 3

Exercise 3
Determine the mean, median, and the standard deviation.
Determine the coefficient of skewness using Pearson's method
Determine the coefficient of skewness using the software method

Listed below are the commissions earned ($000) last year by the sales representatives at the Furniture Patch, Inc.
$3.9 $5.7 $7.3 $10.6 $13.0 $13.6 $15.1 $15.8 $17.1
17.4 17.6 22.3 38.6 43.2 87.7

Exercise 4
A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 537 exchange?

Solution Summary

This solution assists in determining the population variance.

The weights of a random sample of cereal boxes that are supposed to weigh one pound are listed here. Estimate the variance of the entire population of cereal box weights with 90% confidence.
1.05 1.03 .98 1.00 .99 .97 1.01 .96

The grades of a sample of 5 students, selected from a large population, are given below.
Grade
70
80
60
90
75
a. Determine a point estimate for the variance of the population.
b. Determine a 95% confidence interval for the variance of the population.
c. At 90% confidence, test to determine if the variance of the populat

Note: Please see the attachment to view the table which is needed for this question.
Question: You invest 30% in Ham and 70% in Cheese. Find the return and variance on the portfolio. You must calculate: expected return for both firms; standard deviation or variance (assume it is a population (n observations)) for both firms;

Find the appropriate minimum sample size: You want to be 95% confident that the sample variance is within 40% of the populationvariance. Sample size must be an integer.

Please explain in steps how to solve this problem.
I have a population of n=5 scores 0, 6, 4, 3, 12
I need to compute mean and standard deviation for the population
u____ o_____
I need to find the z score for each of the population, and transform the original population into a new population of n= 5 scores with a me

If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.
Note: Variance is the square of the standard d

The following hypothesis are given.
H0: σ2/1 ≤ σ2/2
H1: σ2/1 > σ2/2
A random sample of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. At the .01 significance level

A dietitian obtains the amounts of sugar (in centigrams) from 100 centigrams (or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit Loops, and 7 others. Those values are listed below. Is the standard deviation of those values likely to be a good estimate of the standard deviation of the amounts of su