1. Unit 2 Sections 2-1 & 2-2

2. 2-1: Introduction  The most convenient way of organizing data is by using a frequency table.  The most useful method of presenting data is by using charts and graphs.

3. What we will be able to do throughout this chapter…  Organize data in to frequency tables.  Present data in charts and graphs.  Graphs include: histograms, frequency polygons, pie graphs, stem and leaf plots Section 2-1

4. 2-2: Organizing Data  Raw Data – data collected in its most original form.  Frequency Distribution –the organization of raw data in table form, using classes and frequency.  Class – a quantitative or qualitative category.  Frequency – the number of data values that occur in a specific class.

5.  Given the following data, we can create a frequency distribution: 1 2 6 7 12 13 2 6 9 5 18 7 3 15 15 4 17 1 14 5 4 16 4 5 8 6 5 18 5 2 9 11 12 1 9 2 10 11 4 10 9 18 8 8 4 14 7 3 2 6 Section 2-2

6. Frequency Distribution Class Limits (in Miles) TallyFrequency 1 – 3 4 – 6 7 – 9 10 – 12 13 – 15 16 – 18 Section 2-2

7. Frequency Distribution Class Limits (in Miles) TallyFrequency 1 – 3||||||||||10 4 – 6||||||||||||| | 14 7 – 9||||||||||10 10 – 12||||||6 13 – 15|||||5 16 – 18|||||5 Section 2-2

8.  The categorical frequency distribution is used for data that can be placed in specific categories (i.e. nominal or ordinal level data).  For example: grades on a test, political party, medals at the Olympics. Section 2-2

9. Activity  Twenty-five army inductees were given a blood test to determine blood type. The data set is: ABBABO OOBABB BBOAO A OOOAB ABAOBA  Construct a frequency distribution for this data. Section 2-2

10. Blood Type of Army Members ClassTallyFrequencyPercent A B AB O Section 2-2

11. Blood Type of Army Members ClassTallyFrequencyPercent A|||||520% B|||||||728% AB||||416% O|||||||||936% Section 2-2

12.  Grouped Frequency Distributions are used when the range of the data set is large.  Classes are grouped, however are larger than one unit.  For example: Ages 10 – 15  Lower class limit – smallest data value that can be included in the class.  Upper class limit – largest data value that can be included in the class.  Class boundaries – numbers used to separate the classes so that there are no gaps in the frequency distribution.  For example: A class from 10 – 15 would have a class boundary of 9.5 – 15.5  Class width – found by subtracting the lower class limit from one class with the lower class limit of the next class. Section 2-2

13. Activity  This data represents the record high temperature in Fahrenheit degrees for each of the 50 states. Construct a frequency distribution for the data using 7 classes. Section 2-2 112100127120134118105110109112 110118117116118122114 105109 107112114115118117118122106110 116108110121113120119111104111 120113120117105110118112114

14. Class Limit Class Boundary TallyFrequencyCumulative Frequency Section 2-2

15. Class Limit Class Boundary TallyFrequencyCumulative Frequency 100-10499.5-104.5||22 105-109104.5-109.5||||||| | 810 110-114109.5-114.5||||||| ||||||| |||| 1828 115-119114.5-119.5||||||| |||||| 1341 120-124119.5-124.5|||||||748 125-129124.5-129.5|149 130-134129.5-134.51150 Section 2-2

16.  Ungrouped frequency distributions are used when the range of data values are relatively small. Section 2-2

17. Activity  This data represents the number of miles per gallon that 30 selected four-wheel drive sports utility vehicles obtained in city driving. Section 2-2 121712141618 161812161715 16121516 1214151215 191316181614

18. Class Limit Class Boundary TallyFrequencyCumulative Frequency Section 2-2

19. Class Limit Class Boundary TallyFrequencyCumulative Frequency 1211.5-12.5||||||66 1312.5-13.5|17 1413.5-14.5|||310 1514.5-15.5||||||616 15.5-16.5||||||| | 824 1716.5-17.5||226 1817.5-18.5|||329 1918.5-19.5|130 Section 2-2

20. Reasons to Use a Frequency Distribution  To organize data in a meaningful, intelligible way.  To enable the reader to determine the nature or shape of the distribution.  To facilitate computational procedures for measures of average and spread. (We will see this in Section 3-2 and 3- 3)  To enable the researcher to draw charts and graphs for the presentation of data (We will see in Section 2-3)  To enable the reader to make comparisons among different data sets.