HW1 - HOMEWORK PROBLEMS #1. Someone asks you what your favorite ________ is. Give THREE FACTS about that favorite and THREE OPINIONS about that favorite. Now, how could the facts or the opinions be misinterpreted? Can \"facts\" be misinterpreted? If this same person asked 20 people about that (your) favorite, what type of data are these, what level of measurement, and what kind of data collection sampling would this be? #2. You are the quality assurance person working an assembly line at a TV manufacturing plant. They produce 1000 TV's a day. How many would you decide needed to be tested and how would you pick them from the line? What type of sampling is this? #3. You are going out to eat. There are three shopping malls nearby and each has up to five restaurants (these restaurants are all different). Here are their customer satisfaction ratings on a scale of up to five +'s (highest satisfaction). (a) What type of data and scale are involved here? (b) Which Mall Restaurant did you pick? WHY? (c) What issues could you encounter with your pick once you got there? Mall 1 Mall 2 Mall 3 (a) ++++ (a) +++ (a) +++++ (b) ++++ (b) ++ (b) ++++ (c) ++++ (c) +++ (c) +++ (d) ++ (d) +++++ (e) +++ #4. Give an example of a \"Convenience\" sample and when it might be actually useful. When might it NOT be useful? #5. Generate 20 RANDOM NUMBERS with 1, 2, and then 3 digits. Find an on-line generator or use Excel's \"rand\" or \"randbetween\" function (ask for numbers (1, 2, and 3 digits) between 0 and 100 and just line them up - no spaces). Now, if you use a random numbers Table you simply get a long string of numbers: We will use the digits of (which is simply the ratio of the circumference of a circle to its diameter) : 3.141592653589793238462643383279502884197 NOW, if you want 20 three-digit numbers, where will you start in this chain to get the first number and then how will you get the other 19? Do it. FYI: the number used in geometry, as in the AREA of a circle = r2 , is a random number in that the numbers never repeat: = 3.141592653589793238462643383279502884197 . . . (If you want a million decimal places check out: www.piday.org/million ) The remaining five (5) HW1 problems follow and are based on the Table below: The RANDOM income & expenses by month (not necessarily typical): MONTH JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC TOTALS MEAN MEDIAN MODE VARIANCE STD DEV INCOME GASOLINE 3200 250 2800 225 2800 260 3000 200 3200 200 3100 175 2600 300 2600 250 2600 260 3100 200 3300 250 3500 275 45700 3808 3800 3500 204470 452 2845 237 250 250 1370 37 FOOD ELECTRICITY 500 700 600 650 550 600 450 550 400 400 450 500 500 600 500 700 375 500 350 450 400 500 600 600 5675 473 475 500 6984 84 6750 563 575 600 9148 96 RENT 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 16800 1400 1400 1400 0 0 CREDIT CARDS 1200 900 800 600 600 450 900 1000 850 1000 800 2000 11100 925 875 900 156136 395 #6. What are the TOTAL of this family's annual expenses ? Are they staying above water? What major expenses are NOT listed in this Table? Still above water? #7. Draw a PIE CHART AND VERTICAL BAR GRAPH showing the total ANNUAL cost split among the three EXPENSE categories: gas, food, electricity (a hand drawing is fine). #8. Draw a STEM & LEAF diagram of the MONTHLY INCOME numbers. Explain how you would handle this if the expenses had more significant digits (e.g., $3189 instead of $3200, etc.). This is a possible shortcoming of displaying data in a stem & leaf diagram) #9. HAND DRAW a DOT PLOT for any one data column. Few seem to get this one right ? Look at the LANE text example. Try putting the $-amounts along the bottom axis and a dot for each time a value occurs above that number. You can do this sideways too (see Lane). #10. SUMMARIZE (in your own words) what each of the data displays (i.e., pie chart, bar graph, stem & leaf, and dot plot) above is BEST suited for and what, if any, are its LIMITATIONS. Which display do you feel gave you the best \"picture\" of the shape of the data distribution and/or the most information about it