Population variance
Not what you're looking for?
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 µ = 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?
Purchase this Solution
Solution Summary
This solution assists in determining the population variance.
Purchase this Solution
Free BrainMass Quizzes
Introduction to Finance
This quiz test introductory finance topics.
Cost Concepts: Analyzing Costs in Managerial Accounting
This quiz gives students the opportunity to assess their knowledge of cost concepts used in managerial accounting such as opportunity costs, marginal costs, relevant costs and the benefits and relationships that derive from them.
Understanding the Accounting Equation
These 10 questions help a new student of accounting to understand the basic premise of accounting and how it is applied to the business world.
Managing the Older Worker
This quiz will let you know some of the basics of dealing with older workers. This is increasingly important for managers and human resource workers as many countries are facing an increase in older people in the workforce
Basics of corporate finance
These questions will test you on your knowledge of finance.