Chapter 2

1. Chapter 2 Graphical Descriptions of Data

2. Section 2.1 Frequency Distributions

3. After collecting the data, we need to organize the data. This chapter will describe different ways to organize the data.

4. Arranging data from least to greatest or vice versa. Ordered array

5. Vocabulary

6. Grouped Ungrouped Each class represents a single value • Classes are ranges of possible values Two types of frequency distributions

7. Step 1: Determine the number of classes. • Normally between 5 and 20, but the classes will be suggested in this lesson. • Step 2: Choose an appropriate class width. • Find the range, then round up. The class width is the difference between lower limits. • Step 3: Find the class limits. • The lower limit is the smallest number that can belong to the class. • The upper limit is the largest number that can belong to the class. • Step 4: Determine the frequency of each class. • Make a tally mark for each piece of data in the appropriate class, then count the tally marks to find the total frequency for each class. Steps to create a frequency distribution

8. Class width = Note: Round in increments of 50 for large data values. Used rounded number for smaller data values. Example

9. The class boundaries split the difference in the gap between the upper limit of one class and the lower limit of the next class. • To find the class boundary, add the upper limit of one class to the lower limit of the next class and divide by two. • Example: Class boundaries

11. The class midpoint is the midpoint of the lower limit and the upper limit. • To find the class midpoint, add the lower and upper limit of the same class, then divide by 2. • Example: • Lower limit = 800 Upper limit = 1099 Class midpoints

13. Relative frequency is the percentage of the data that falls in a particular class. • Sample size is the total amount of data values. Relative frequency

15. Cumulative frequency is the sum of the frequency for a given class and the frequencies of all previous classes. • The cumulative frequency of the last class should equal the sample size. Cumulative frequency

16. Practice problem

17. Solution

18. Section 2.2a Graphical Displays of Data: Pie Charts and Bar Graphs

24. Pie chart

28. A bar graph that puts the data in descending order. Pareto chart

29. Represents two sets of data, with bars next to each other. Side-by-side bar graph

30. Represents two sets of data by stacking the bars. Stacked bar graph

32. Section 2.2b Graphical Displays of Data: Histograms, Polygons, and Stem and Leaf Plots

36. Similar to the histogram, except the height of the bars is the relative frequency instead of the frequency. Relative frequency histogram

37. Step 1: Mark the class boundaries on the x-axis and the frequencies on the y-axis. There will be two extra classes, one on the lower end and one on the upper end, both with a frequency of 0. How to create a frequency polygon

38. Step 2: Add the midpoint to the x-axis, then plot a point at the frequency right above the midpoint. • Step 3: Join each point with a line segment.

39. An ogive is a line graph that uses the boundaries and the cumulative frequency of the data. Ogive (“oh-jive”)

41. OR

42. Similar to the stem and leaf other than it is a number line with dots representing the leaves. Dot plot

44. Section 2.3 Analyzing Graphs

48. Time-Series Graph – a picture of how data changes over time and has a variable of time as the horizontal axis.

49. Cross-Sectional Graph – a picture of the data at a given moment in time. Neither axis will have a variable of time