135 Homework 6.2 Measures of the Spread

Homework 6.3: Measures of the Spread of Data You should complete the homework assignment by the due date in Blackboard. Failure to submit the homework by 11:59 PM on the due date will result in a zero on the assignment. Remember that copying another student’s assignment, having someone else complete your assignment, or downloading answers from online are all academic misconduct and will result in a 0 on the assignment. You MAY work together with other students, but you should submit all of your own work. You should show all work on every problem – failure to do so may result in zero credit on the problem. Use this data for problems 1 and 2. A researcher collects the salaries (in thousands of dollars) of 20 college classmates 5 years after they graduated: 38 47 29 18 56 43 38 42 68 52 47 53 41 36 45 78 51 38 39 43 1. What is the mean? What is the standard deviation? 2. If data is normally distributed, 95% of the values (19 out of 20) will be within 2 standard deviations of the mean. Calculate two standard deviations below and above the mean. Are 95% of the values in this range? Use the frequency table given below for problems 3 and 4. Consider the data given in the frequency table below: Value Frequency Relative Frequency Cumulative Relative Frequency 1 4 2 26 3 42 4 18 5 20 3. Compute the relative and cumulative relative frequencies to fill in the rest of the table. Find the mean. 4. Find the standard deviation.

5. Calculate the standard deviation for the data set with these frequencies: Value Frequency 1 10 2 20 3 30 4 40 6. The CDC says that the mean height for a 3 year old boy in the USA is 96 cm, with a standard deviation of 3 cm. Fill in the blanks in the sentences below. a. A 100 cm tall 3 year old boy is ______ standard deviations ______ the mean. b. A 92 cm tall 3 year old boy is ______ standard deviations ______ the mean. c. A _______ cm tall 3 year old boy is 2.5 standard deviations below the mean. Use the data in this table to answer questions 7 and 8. When choosing between job offers, where the job is located can make a big difference. The same salary in New York City, for example, is harder to live on than in Nashville, because the cost of living is much higher. A recent college graduate is trying to choose between three jobs, all of which pay $50,000 a year. The jobs are located in three different cities. In those three cities, the mean and standard deviations of salaries are as follows: City Mean Salary Standard Deviation City A $44,000 $4000 City B $47,000 $1200 City C $41,000 $6000 7. Compute the z-score of the $50,000 salary in each city. 8. Rank the cities from lowest to highest z-score. In which city will the $50,000 salary go the farthest? In which will it go the least far? Use the information in this table for problems 9 and 10. Devon is shopping for a car. They find five different cars for sale and want to know which one is the best deal. They do a search online and compute the mean and standard deviation for the price of each car. Car Sale Price Mean Price Standard Deviation Red Truck $26,000 $28,500 $1000 Grey SUV $29,000 $31,000 $2000 Green Coupe $15,000 $16,400 $1200 Black Sedan $22,500 $23,800 $700 Orange Sportscar $54,000 $57,000 $2800 9. Compute the Z-score for each sales price.