The first 3 assignments will reinforce the concepts of mean, median, mode and standard deviation and their real world applications. Click on the following links to display the assignments.

1. A small company pays its president $200,000.00. The vice-president gets $150,000. The foreman earns $30,000.00. There are three workers in the company, earning $25,000, $22,000, 22,000 respectively. The secretary earns $19,000.

   a). Find the mode, median, mean income in this company.

   b). The union representative wants to negotiate new wages. In this negotiation would he emphasize mode, median or mean? Explain why in a paragraph.

   c). Which of the three measures would the president of the company stress in the negotiations? Explain why in a paragraph.

   d). Which do you think best represents this sample? Explain why in a paragraph.

   e). Can you say that the measure you chose in #4 is always best to use? Explain why or why not in a paragraph

    

2. Let us suppose the income distribution of the U.S. is given by the graph below:

a). Which of the three best describes the income distribution of the U.S. population?

b). Write a paragraph explaining why the measure you chose as your answer (to part a) is appropriate. (Hint: You may discuss skewedness as well as resistant measure) [Top]

Describe in your own words what mean and standard deviation indicate. Give examples. (Note: You are not asked to describe how mean and standard deviation are calculated.) [Top]

1. Drug X has standard deviation of 3 days recovery time. Drug Y has standard deviation of 7 days recovery time. Based solely on this information which of the following statements is true?
   
   
   a) Drug X is a better drug than drug Y.
   
   b) Drug Y is a better drug than drug X.
   
   c) Drug X and drug Y are equally good.
   
   d) No decision can be made.
   
   
2. Given the standard deviation above, suppose drug X has mean recovery time of 30 days and drug Y has mean recovery time of 15 days. Explain which drug is better.
   
   
3. Given the standard deviation above, suppose drug X has mean recovery time of 8 days and drug Y has mean recovery time of 20 days. Explain which drug is better.
   
   
4. Looking back on your answers to previous questions, write a paragraph about reaching a decision based solely on standard deviation [Top]

1. Explain in your own words what it means for two events to be independent. (You are not asked to give a formula.) Give an example
   
   
2. Explain in your own words what it means for two events to be dependent. (You are not asked to give a formula.) Give an example.
   
   
3. Explain in your own words what it means for two events to be mutually exclusive. Be sure to use the concepts of dependence and independence, which you have used in part A, and B, in explaining mutually exclusive events. Give an example. [Top]

It is impossible to set up a table of areas under the normal curve for each different mean, m, and standard deviation, s, combination. Clearly one way to get around that is to standardize the distribution so that we can use one table of areas for all normal distributions.

1. Suppose that Tom and Diane are enrolled in two different sections of Statistics I (MAT120). Assuming large class size, and the scores on the first exam follow a normal distribution. In Tom’s section, the average is 60 and his score is 72. In Diane’s section, the average is 71 and her score is 83. Both are happy because their scores are 12 points above the average of each respective section. Who did better and why?
   
   
2. Suppose now the standard deviation in Diane’s and in Tom’s section was s = 6.4 and s=6.5 respectively …[Top]

Describe in your own words the (celebrated) Central Limit Theorem. What assumptions must be met in order to use its conclusions? Give an example of a situation where the Central Limit theorem may fail because of unmet assumptions.[Top]

Compare the graph of the normal distribution of x (whole population) to the graph of the normal distribution of (means of the samples that are taken, that is, sample means). In your discussion be sure to include comparison of the means, standard deviations. Could the two curves coincide exactly? [Top]

Cancer patients using a certain treatment have an average survival time of 2 years with a standard deviation of 4 months. A physician claims that his new method of treatment increases the average survival time of patients, while keeping the standard deviation the same.

100 randomly chosen patients who received this new treatment had an average survival time of 26 months.

1. What is the probability that 100 randomly chosen patients had an average survival of 26 months or more?
   
2. Interpret the result of problem 1 in a paragraph, defending your reasoning whether the claim that the new treatment is more effective or is bogus (not more effective). [Top]