Organizing Data into Frequency Distributions and Graphs, Study Guides, Projects, Research of Probability and Statistics

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Chpt 2.

Frequency Distributions and Graphs

2-2 Data Collection and Sampling Techniques.

1

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Homework

2-2 Read pages 34-

p43 Applying the Concepts

p43 1-7, 12, 13

Chpt 2.

/ into frequency distribu5ons Organizing Data An ungrouped frequency distribution is simply each score listed in a table next to the frequency of the occurrence of that datum value. Once you have collected a bunch of raw data, what should you do with it? The first step in statistics is to draw a picture of the data. To do that the data must be organized in some fashion. The most basic organization is a frequency distribution.

/ into frequency distribu5ons Organizing Data Ungrouped Frequency Distributions - used for data that can be enumerated and when the range of values in the data set is not large. number of miles teachers drive from home to school number of girls in a 4 child family number of pets owned by student families, etc.

/ into frequency distribu5ons Organizing Data If our variables are categorical and the data is nominal, or ordinal, the distribution is called, appropriately, a Categorical Frequency Distribution. Personality tally Frequency (f) A |||||||||||||| 17 B ||||||||| 11 A/B |||||||||||||||||| 22 If we list subjects by personality type we might see:

/ into frequency distribu5ons Organizing Data Twenty-five army inductees were given a blood test to determine blood type. Raw Data: A, B, B, AB, O O, O, B, AB, B B, B, O, A, O A, O, O, O, AB AB, A, O, B, A Type tally Frequency (f) O A B AB IIIIIIIII IIII IIIII III I II I 9 5 7 4 The tally marks are not a necessary part of the frequency table. They are only to help with accuracy.

/ into frequency distribu5ons Organizing Data Class limits represent the largest and smallest data values that an be included in the class. Class limits are actual data values. Class boundaries provide values that eliminate gaps bet ween the classes in the frequency distribution. Class boundaries are one decimal place more accurate than the data. Class boundaries are not actual data values. For this course, class boundaries will always end with a 5. To find a class boundary, average the upper class limit of one class and the lower class limit of the next class.

/ into frequency distribu5ons Organizing Data The class limits define the class and are actual data values. Class limits are possible data values. Class boundaries are not possible data values but define the intervals within which the data values must fall. The class boundaries are ½ an interval above and below the class limits.

/ into frequency distribu5ons In the age class 0 – 4, the class limits 0 and 4 are actual data values. Age 4 represents the ages 3.5 to 4.5, including 3.5 and not including 4.5. (i.e. [3.5, 4.5)). Thus the class boundaries of 0 – 4 are actually -0.5 to 4.5. The class boundaries for the class 5 – 9 are 4.5 and 9.5. Relax … the -0.5 is a boundary and cannot be a data value. Age Tally Frequency 0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29

/ into frequency distribu5ons Organizing Data Now our Grouped Frequency Distribution might look like: Age - limits Age - Boundaries Tally Frequency 0 - 4 -0.5 - 4. 5 - 9 4.5 – 9. 10 - 14 9.5 – 14. 15 - 19 14.5 – 19. 20 - 24 19.5 – 24. 25 - 29 24.5 – 29.

/ Objec&ve : Organizing data into frequency distribu5ons Rules for setting class width

2. Class width must be consistent (with one exception).
3. No overlapping intervals (classes). The classes must be mutually exclusive and exhaustive. One datum cannot belong in t wo classes and all data is included. Organizing Data
4. The class width should be small enough to accurately portray the data but large enough to keep the number of classes manageable. Readers of the data cannot assimilate too many classes, the forest gets lost in the trees. The number of classes is best kept bet ween 5 and 15. Fewer than 5 and the trends get lost, more than 15 and the information becomes lost. This rule is not cast in stone. I try to limit to bet ween 7 and 12 depending on the data. (14 - 10 + 1 = 5) Class width = upper boundary – lower boundary.^ (14.5 - 10.5 = 5) Class width = upper limit – lower limit + 1 interval Age - limits Age - Boundaries Tally Frequency 0 - 4 -0.5 - 4. 5 - 9 4.5 – 9. 10 - 14 9.5 – 14. 15 - 19 14.5 – 19. 20 - 24 19.5 – 24. 25 - 29 24.5 – 29.

/ into frequency distribu5ons

4. The whole idea of a frequency distribution is to provide an accurate and easily understood picture of the data as simply as possible.
5. If the class width is an odd number the midpoint of the class is an actual datum value. That can be useful for graphical representations of the data. Not a necessary condition but often useful because we like pretty pictures of our data. Organizing Data Rules for setting class width

/ into frequency distribu5ons Example In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes.

/ into frequency distribu5ons Step 2: Find the range: R = 22 -^ 5 = 17. Step 3: Select the number of classes desired. In this case we are told to create 6 classes. Step 4: Find the class width by dividing the range by the number of classes. Width = 17/6 = 2.83. This value is rounded up to 3. Step 1: Find the highest and lowest values: High = 22 and Low = 5. Step 5: Select the starting point, we will start with the lowest value 5. Organizing Data