Unit 2A Review Packet Name ______________________________________ 1. Peter and Chris Griffin go to a hot dog eating contest. The following data shows how many hotdogs each person ate in 1 hour. Hot Dogs Eaten in One Hour 83 76 90 58 66 44 86 66 61 59 50 53 a. Construct a histogram that displays these results. 61 64 Hotdogs 73 Frequency b. Construct a relative frequency histogram based on the same data. Hotdogs Frequency Rel. Frequency c. Describe the distribution. (Hint: spread, outliers, center, shape SOCS) d. Find the median number of hotdogs these 15 contestants ate in the competition. e. The mean hotdogs for these 15 contestants is 66 hotdogs. Herbert took this challenge. The mean of all 16 contestants is now 66.5. What was Herbert’s score? 2. Two cities: Petersburg and St. Lewis, have different populations and growth rates. Petersburg had a population of 150,000 in 2012 and grows at a fast rate of 2.3%. St. Lewis had a population of 165,000 in 2012 and grows at a slow rate of .2% a.)Write out a NOW-­‐NEXT that can be used to get the Next years population based on the population right NOW for each city. NOW-­‐NEXT for Petersburg: NOW-­‐NEXT for St. Lewis: 3. Make a histogram and a relative frequency histogram for the data below: Number of Free Throws 0-­‐1 2-­‐3 4-­‐5 6-­‐7 8-­‐9 10-­‐11 12-­‐13 13-­‐14 Frequency 1 5 10 4 0 0 0 2 a. Based on your histograms, would you say the mean and median were the approximately the same, or are they different? Explain your choice. 4. On the first three tests, Christina has scores of 85, 90, and 75. What is the lowest possible score that she can score on the fourth test in order to have a mean of 85? Simplify the following expressions, then tell what subset that number belongs to. 5. -­‐3 + 5(5 – 3)3 ÷ 4 !
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6. + 4 − 7. If a data distribution contains 135 values, at what position would we find the median (don’t just say the middle)? 8. Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13 Mean: _____________ Mode _______________ Median:____________ Range _______________ 9. Using the same data above, add a number that will increase the mean, but keep the median the same. Show or explain your work. 10. The following relative frequency table displays the amount of siblings that twenty students have. Number of siblings 0 1 2 3 4 5 Relative Frequency 0.2 0.4 0.25 0.1 0 0.05 a) What percent of students have 3 siblings?
b) What percent of students have at least 2 siblings?
c) How many of the students have 1 sibling?
11. Sketch an example of: Approximately Normal Skewed Right Skewed Left 12. On the above sketches, draw a line to show where the mean and median would fall for each distribution. Is the mean or median more resistant to outliers? 1 13. The following frequency table displayed the scores students made on a recent math test. a. How many students were included in the data? Score Frequency 70 4 75 5 80 7 85 7 c. What is the mean of the data? 90 2 b. What is the median of the data? 14. The measure of central tendency that is affected by an extreme value, also known as an ________________, is the _______________, while the ____________________ is resistant, meaning it isn’t easily affected by extreme values 15. The dot plot to the right shows the average hours of sleep students get each night. a) How many students were surveyed? b) What percent of students get at least 6.5 hours of sleep a night? c) How would you describe the distribution (SOCS)? d) If an extra data value, 1, was added to the dot plot, how would it affect the mean? How would it affect the median? Would you describe this number as an outlier, why or why not.