Rec 3B_Boxplots and Stat Crunch

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1430.01

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Feb 20, 2024

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STAT 1430 Recitation 3B SD and Boxplots Hot Dog Eating Contest • Log into MyStatLab • Click on the Stat 1430 course • Click on StatCrunch on the left side menu. • Click on “Visit the StatCrunch website ” • Click on “OPEN STATCRUNCH” on the menu bar at the very top. This will open a blank spreadsheet for you to enter data into. • E nter the numbers from the results section of the following WIKI site to create a data set showing the year, gender, and number of Hot Dogs eaten by the Winner of Nathan’s Famous Hot Dog Eating Contest, from 2011-2019. http://en.wikipedia.org/wiki/Nathan's_Hot_Dog_Eating_Contest The first rows of your data set should look like this (click on the top row of the StatCrunch spreadsheet to change variable names): YEAR GENDER # HOT DOGS 2011 M 62 2011 F 40 Questions: 1. Using Statcrunch, find the 5-number summary (STAT/Summary Statistics/Columns) for MEN ONLY. Then do it for the women. Do you see any differences? (Units are number of hotdogs) MEN 5 # Summary: Min:61 Q1:62 Median:69 Q3: 71 Max:74 WOMEN 5 # Summary: Min:31 Q1:36.75 Median:38 Q3:40

STAT 1430 Recitation 3B SD and Boxplots Max:45 Difference ： The number of hot dogs for women is almost always half that of men 2. Make boxplots from your data that are side by side on the same graph that compare the women to the men. Use the directions below: TO MAKE BOXPLOTS USING STATCRUNCH: -Go to GRAPH / BOXPLOT -SELECT COLUMN (variable) to make your boxplot out of (#hotdogs) -GROUP BY: the gender variable -COMPUTE! 3. Interpret the boxplot for men in terms of shape, center, and variability. Use language that a non-statistician would understand. Do the same for the women. The center is the red line in the picture, which is 69; this means that in the ranking, the person in the middle of the pack ate 69 hot dogs over the past eight years, it is so much! And the variability is the distance between two sides of a rectangle, which refers to the Stability of data. The distance is long, so this data set is not very uniform.

STAT 1430 Recitation 3B SD and Boxplots The center is the red line in the picture, which is 38; this means that in the ranking, the person in the middle of the pack ate 38 . This also shows that women have eaten much less than men And the variability is the distance between tw. sides of a rectangle, which refers to the Stability of data. The distance is long, so this data set is Relative stable. 4. Describe the differences between the results of the men vs women by comparing your boxplots. Nathan’s Famous Hot Dog Eating Contest Official Website: http://www.nathansfamous.com/contest STANDARD DEVIATION 5. Suppose at the end of the year everyone at Bob’s restaurant gets a $5.00 raise per hour to their existing wages. How does this raise affect the standard deviation of their wages? a. SD is larger than before b. SD is smaller than before c. SD is same as before 6. Suppose at the end of the year everyone at Bob’s restaurant gets a 5 PERCENT raise per hour to their existing wages. How does this raise affect the standard deviation of their wages? a. SD is larger than before b. SD is smaller than before c. SD is same as before Next 3 problems: The starting salaries (in dollars) of a random sample of all graduates from OSU from the year 1970 were analyzed. The results are shown below.

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STAT 1430 Recitation 3B SD and Boxplots Total Variable Count Mean St.Dev. Variance Min. Q1 Median Q3 Max. Salary 125 24329 2164 4683459 18958 22663 24461 26155 28123 7. Why would you say this data set is fairly symmetric? a. The mean and median are close a. The standard deviation is small compared to the mean and median b. Both a and b c. Not enough information to tell 8. What units is the standard deviation in? d. No units b. Dollars c. Years 9. Suppose after taking the sample, the program finds that their next graduate starts at $35,000 per year. Which of the following statistics will be the least affected by adding this graduate to the data set? a. The mean b. The median c. The standard deviation d. All of these will be affected the same amount 10. A small data set was summarized using statistics software; the output is below. Which of the following data sets matches these descriptive statistics? Descriptive Statistics: Quiz Score Variable Count Mean St.Dev. Quiz 6 1.0000 0.00000000 a. 1, 2, 3, 4, 5, 6 b. 3, 3, 3, 3, 3, 3 c. 1, 1, 1, 1, 1, 1 d. Could be more than one possible answer BOXPLOTS For the next 3 problems: The number of robberies each year was recorded for each of two banks over a 20-year period. The boxplots are shown below.

STAT 1430 Recitation 3B SD and Boxplots Robberies B A 7 6 5 4 3 2 1 11. Which of the following statements must be true? a. Bank B had more robberies in general than bank A over these 20 years. b. Bank B had fewer robberies in general than bank A over these 20 years. c. Both banks had the same number of robberies over these 20 years. 12. The amount of variability in number of robberies based on these boxplots must be: a. The same for both banks b. Smaller for bank A than for bank B c. Larger for bank A than for bank B d. Not enough information to tell. 13. Based on the information above, which of the following statements is true? a. During 50% of the years bank A had 3 or more robberies b. For 10 of the years bank A had between 2 and 4 robberies c. Both a and b are true d. Both a and b are false Next 4 problems: A taxi cab company takes a random sample of 50 of its taxis and notes their miles per gallon (mpg) on a test run. The computer output is shown below. Descriptive Statistics: MPG Variable Count Mean St.Dev. Min. Q1 Median Q3 Max. Mileage 50 19.784 3.093 13.300 17.800 20.000 21.825 26.000 14. The number of miles per gallon that marks the 75 th percentile is 21.825. a. True b. False 15. What is the IQR for this data set? _____4.025__________________ 16. 75% of the taxis have a MPG higher than what value?

STAT 1430 Recitation 3B SD and Boxplots a. 26.000 b. 17.800 c. 21.825 d. None of the above 17. When skewness is present in a set of data, which of the following descriptive summary measures are most appropriate? a. Mean and standard deviation b. Maximum and minimum c. Interquartile range and median d. Mean and interquartile range 18. Which of the following descriptive statistics based on the above data is in units of MPG? LIST ALL THAT APPLY! a. Mean b. Median c. IQR d. Standard Deviation 19. Suppose everyone at Bob’s restaurant gets a $5.00 raise per hour to their existing wages. How does this raise affect the Interquartile Range of the salaries? a. It will be larger than before b. It will be smaller than before c. It will be the same as before 20. Suppose at the end of the year everyone at Bob’s restaurant gets a 5 PERCENT raise per hour to their existing wages. How does this raise affect the Interquartile Range of their wages? (Hint: what are you doing to the data when you give a 5% raise?) a. It will be larger than before b. It will be the same as before c. It will be smaller than before Next two problems: A survey of 15 randomly selected employees from Bob’s factory was taken to find out how many sick days they took due to colds and flu last year. A boxplot and some descriptive statistics for the data are shown below. Variable N Mean SE Mean St.Dev. Min. Q1 Median Q3 Max. Sick Day 15 6.00 1.10 4.28 0 3.00 5.00 9.00 15.00

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STAT 1430 Recitation 3B SD and Boxplots Sick day 16 14 12 10 8 6 4 2 0 Boxplot of Sick day 21. The 25th percentile is: a. Around 5 b. Around 3 c. Around (9-5)/2 = 4.5 d. Around 9 22. According to the boxplot above, the shape of this data set is: a. Skewed right b. Skewed left c. Symmetric d. Can’t tell