# Box

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## Box

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1. Box and Whisker Plot

2. Median: the middle of the data, after the numbers have been put into order Example: 1, 7, 2, 8, 4, 6, 3, 9, 5 1, 2, 3, 4, 5, 6, 7, 8, 9

3. Lower Quartile (LQ): median of the lower half of the data set [1, 2, 3, 4,] 5, 6, 7, 8, 9 Since 2 and 3 are in the middle of the lower half of the data set we average the two to get a Lower Quartile of 2.5

4. Upper Quartile (UQ): The median of the upper half of the data set 1, 2, 3, 4, 5, [6, 7, 8, 9] Since 7 and 8 are in the middle of the upper half of the data set we average the two to get a Upper Quartile of 7.5

5. Lower Extrema: The least, lowest value in the data set 1, 2, 3, 4, 5, 6, 7, 8, 9

6. Upper Extrema: The highest, greatest value in the data set

7. Interquartile Range: the difference between the upper and lower quartiles Upper Quartile – Lower Quartile = Interquartile Range Upper Extrema Lower Extrema [1, 2, 3, 4,] 5, [6, 7, 8, 9] 5 UQ – LQ = 7.5 - 2.5 = Range: the difference between the upper and lower Extrema 8 9 – 1 =

8. If you took the data set: 1, 2, 3, 4, 5, 6, 7, 99 Outlier: an observation that lies outside the overall pattern of a distribution

9. Process: 1>>Put the numbers within the data set in numerical order. 2>>Find the Median (the middle number) 3>>Find the Upper and Lower Quartiles (the median of the Upper and Lower halves of the data set) 4>>Find the Upper and Lower Extrema (The first and last number of the data set) 5>>Find the Interquartile Range (UQ-LQ) 6>>Any Outliers?

10. Lets build one together: 19, 7, 12, 3, 5, 18, 6, 8, 7, 11, 1, 4, 20, 14, 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

11. Directions: Given the data set on your paper find the: >Median >Lower Quartile >Upper Quartile >Lower Extrema >Upper Extrema >Range Plot the points on the Number line and create your Box-and-Whisker plot

12. Stem &Leaf

13. Stem-and-leaf-plot: Data is organized in a chart from least to greatest Stem Leaf Leaves: the digits of the least place value Stems: the next place value digits 2 3 6, 8, 9 1, 2 leaf Stem 26= 2 | 6 28= 2 | 8 29= 2 | 9 31= 3 | 1 32= 3 | 2

14. 12 17 23 14 How many numbers are represented by the stem-and-leaf-plot? 2 6 7 3 3 5 1 9 4 7 2 7 1 2 3 4 5 6 25 39 16 67 Stem Leaf 31 23 44 18 What is the mean of the data? 16 62 35 47 What is the median of the set of data? What is the range of the set of data? What is the mode of the data? Key 1|2 = 12

15. Group B Group A 9 9 9 5 9 9 5 3 9 8 6 4 2 9 7 5 3 1 0 0 6 7 8 9 10 3 8 9 9 2 5 8 9 0 3 7 9 9 1 4 4 4 8 0 0 Key 6|3=63 Group A Group B Conclusion Mean Median Mode Range # of data

16. Frequency Tables

17. Frequency Table: Display of data which falls within given intervals >>>Must have an Interval and scale, in which the intervals must be equal. Scale for which you split up the data. Tally The totals of the tally's, representing the data given Interval # number Frequency IIII Data #, #, #, #, # #, #, #, # #, #, #, #, # #, #, #, # #, #, #, #, # IIII IIII

18. The number of calls from motorists per day for roadside service was recorded for the month of December 2003. 0-39 40-79 80-119 120-159 160-199 200-239 1 5 12 8 4 1 I IIII IIII IIII II IIII III IIII I Calls Daily Tally Frequency What does the Frequency on the graph represent? How many days were there between 80-119 calls made? Which two intervals had the least amount of days in which calls occured? How many days were in the month of December in 2003? How many days were there 120 or more calls made?

19. Movie Rentals within a Month: 10, 9, 2, 17, 12, 9, 11, 10, 4, 14, 3, 15, 0, 6, 5, 9, 20, 10, 11, 8, 3, 1, 13, 4 Remember: Intervals must be equal 0-4 5-9 10-14 15-19 20-24 IIII II IIII I IIII III II I 7 6 8 2 1 Interval # Movies Frequency How many customers rented movies this month? What is the interval of the frequency table? How many customers rent between 0-14 movies a month?

20. B A R Graphs

21. Bar Graph: Is a graph that uses rectangular bars, with lengths proportional to the values which they represent, to symbolize a set of data. The bars can be plotted vertically or horizontally. Favorite Sport Vertical Axis 10 8 Number of Students 6 4 Horizontal Axis 2 0 Soccer Softball Basketball Football Other Sports

22. What is represented by the graph? 12 How many students were included in the survey? What is represented by the horizontal axis? Eye Color What is the vertical axis representing? 10 8 What were the top two groups represented by the graph? Number of Students 6 4 How many students were represented by these two groups? 2 0 How many fewer green eyed students are there than blue eyed students in the class? Brown Blue Green Other Color

23. 65 year olds 45 year olds 25 year olds Year Youth Vote vs. Everyone Else 2008 0 10 20 30 40 50 60 Percentage voting Republican 2004 Which group decreases in percentage voting as the years go on? What is being compared in this graph? 2000 What three groups are represented on the graph? What could be concluded from this graph?

24. Histograms

25. Histogram: A special kind of bar graph which uses bars to represent the frequency of numerical data after the data has been organized into intervals. Grades Tally Frequency 61-70 71-80 81-90 91-100 III IIIII IIIII IIIII IIIIIIIIIIIIIII IIIII IIIIIIIIII III 3 10 20 18 First, you must have a frequency table [must include interval, tally marks, frequency]

26. Grades Tally Frequency III IIIII IIIII IIIII IIIIIIIIIIIIIII IIIII IIIIIIIIII III 61-70 71-80 81-90 91-100 3 10 20 18 25 20 Number of Students The Histogram contains data on the test scores students made on their latest math test. Use the graph to answer the following questions. 15 10 5 0 What does the Horizontal axis represent? 61-70 71-80 81-90 91-100 Test Grades What does the vertical axis represent? How many grades are represented by the Histogram? How many students received a grade of 81 or higher? What was the lowest test grade a students could have made on this test given the data?

27. Dot, LinePlot

28. Line Plot: A diagram that shows the frequency of data on a number line. X X X X X XXXXX X XXXXXXXXXX X X X XXXXXXXXXXXXXXXX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

29. Cluster: group that is close together X X X X X XXXXX X XXXXXXXXXX X X X XXXXXXXXXXXXXXXX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Outlier: number or numbers that are fairly distant from the rest of the set of data X X X X X X X X X X XXXXXX X XXXXXXXXX X X X XXXXXXXXXX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

30. Range: The difference between the largest and smallest numbers in the data set. X X X X X XXXXX X XXXXXXXXXX X X X XXXXXXXXXXXXXXXX 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ___-___ =___

31. The Pep club is selling candy bars in boxes of 25. Mrs. Taylor has a list of how many candy bars each member has sold so far. The results are represented in the line/dot plot below. X X X X XXXX X XXXXXXXX X XXXXXXXXXX X XXXXXXXXXXXXXXXXXXX How many students have sold more than 15 candy bars? Are there any outliers in this set of data? How many students in the pep club have sold at least 1 candy bar? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 What is the range of this set of data?

32. Graph A The Mean of which graph is greater? X X XX X XXXXXXXXXX Which graph has the smallest Median? 0 2 4 6 8 10 12 14 16 18 20 22 Graph B Which graph has the largest mode? What is that mode? X X X XX X XXXXXXXXX 0 2 4 6 8 10 12 14 16 18 20 22 Which graph has the largest Range?

33. Line Graph

34. Line Graph:  A graph that uses points connected by lines to show how something changes in value 12.50 Vertical Axis 11.50 10.50 Hourly Rate 9.50 8.50 Horizontal Axis 7.50 6 12 18 24 30 36 Months

35. What does the graph represent? 12.50 If the trend of the graph were too continue what would you expect the Hourly rate to be at 42 Months? 11.50 10.50 Hourly Rate 9.50 How would you best describe the trend of the data? Increasing or decreasing? At what rate? 8.50 7.50 6 12 18 24 30 36 Months

36. Employee A Employee B Shared intervals What do the orange points on the graph represent? 12.50 11.50 What differences can be seen between Employee A and Employee B? 10.50 Hourly Rate 9.50 8.50 If the trend continues how much will Employee B be making in 42 months? 7.50 6 12 18 24 30 36 Months