1. Section 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

2. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Ordered array – an ordered list of the data from largest to smallest or vice versa. Distribution – displays data values that occur and how often they occur. It can be a chart or a table. Frequency Distribution – table that divides data into groups, called classes, and shows how many data values occur in each group. Frequency, f – number of data values in a class. Organizing Data:

3. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists 1.Decide on the number of classes Between 5 and 20 2.Choose an appropriate class width 3.Find the class limits Start with the lowest value and add the class width to get the next class limit. 4.Determine the frequency of each class Count the number of data values in each class. Creating frequency tables:

4. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists 1.Classes boundaries Split the difference in the gap between the upper limit of one class and the lower limit of the next class. 2.Midpoints 3.Relative Frequency 4.Cumulative Frequency The sum of the frequency for a given class and all previous classes. Other characteristics can be calculated once the basic frequency table has been constructed:

5. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Create a frequency distribution using 5 classes: Quiz Grades 93547 810867 45278 79 1 86 98 Solution – First place the data in an ordered array: Quiz Grades – Ordered Array 12344 55667 77788 88899 910

6. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Since we have the smallest and largest values, we can find the class width. Round 1.8 up to a sensible value, 2. Next begin building the class limits with the smallest data value in the set. Solution – continued:

7. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists The frequency distribution: Quiz Grades Classf Class Boundaries Midpoint Relative Frequency Cumulative Frequency 1 – 220.5 – 2.51.52 3 – 432.5 – 4.53.55 5 – 644.5 – 6.55.59 7 – 896.5 – 8.57.518 9 – 107 8.5 – 10.59.525

8. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Create a frequency distribution using 6 classes: GPA’s 3.22.62.92.03.1 3.51.81.33.83.0 1.12.02.53.13.4 Solution – First place the data in an ordered array: GPA’s – Ordered Array 1.11.31.82.0 2.52.62.93.03.1 3.23.43.53.8

9. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists Since we have the smallest and largest values, we can find the class width. Round 0.45 up to a sensible value, 0.5. Next begin building the class limits with the smallest data value in the set. Solution – continued:

10. Graphical Descriptions of Data 2.1 Frequency Distributions HAWKES LEARNING SYSTEMS math courseware specialists The frequency distribution: Quiz Grades Classf Class Boundaries Midpoint Relative Frequency Cumulative Frequency 1.0 – 1.420.95 – 1.451.22 1.5 – 1.911.45 – 1.951.73 2.0 – 2.421.95 – 2.452.25 2.5 – 2.932.45 – 2.952.78 3.0 – 3.452.95 – 3.453.213 3.5 – 3.923.45 – 3.953.715