Section Frequency Distribution and Statistical Graphs. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Transcription

1 Section 13.3 Frequency Distribution and Statistical Graphs

2 INB Table of Contents Date Topic Page # July 7, 2014 Section 12.1 & 12.2 Worksheet 58 July 7, 2014 Shoe Probability Project 59 July 7, 2014 Conditional Probability Worksheet 60 July 7, 2014 Blank Page 61 July 7, 2014 Section 13.3 Examples 62 July 7, 2014 Section 13.3 Notes

3 What You Will Learn Frequency Distributions Histograms Frequency Polygons Stem-and-Leaf Displays Circle Graphs

4 Frequency Distribution A piece of data is a single response to an experiment. A frequency distribution is a listing of observed values and the corresponding frequency of occurrence of each value

5 Example 1: Frequency Distribution The number of children per family is recorded for 64 families surveyed. Construct a frequency distribution of the following data:

6 Rules for Data Grouped by Classes 1. The classes should be of the same width. 2. The classes should not overlap. 3. Each piece of data should belong to only one class. 4. There should be 5 12 classes

7 Definitions Classes Lower class limits Upper class limits Midpoint of a class is found by adding the lower and upper class limits and dividing the sum by

8 Example 2: A Frequency Distribution of Family Income The following set of data represents the family income (in thousands of dollars, rounded to the nearest hundred) of 15 randomly selected families. Construct a frequency distribution with a first class of

9 Histograms A histogram is a graph with observed values on its horizontal scale and frequencies on its vertical scale. Because histograms and other bar graphs are easy to interpret visually, they are used a great deal in newspapers and magazines

10 Constructing a Histogram A bar is constructed above each observed value (or class when classes are used), indicating the frequency of that value (or class). The horizontal scale need not start at zero, and the calibrations on the horizontal and vertical scales do not have to be the same

11 Constructing a Histogram The vertical scale must start at zero. To accommodate large frequencies on the vertical scale, it may be necessary to break the scale

12 Example 3: Construct a Histogram Use the frequency distribution developed in Example 1 to construct a histogram of this frequency distribution

13 Frequency Polygon Frequency polygons are line graphs with scales the same as those of the histogram; that is, the horizontal scale indicates observed values and the vertical scale indicates frequency

14 Constructing a Frequency Polygon Place a dot at the corresponding frequency above each of the observed values. Then connect the dots with straight-line segments

15 Constructing a Frequency Polygon When constructing frequency polygons, always put in two additional class marks, one at the lower end and one at the upper end on the horizontal scale. Since the frequency at these added class marks is 0, the end points of the frequency polygon will always be on the horizontal scale

16 Example 4: Construct a Histogram Construct a frequency polygon of the frequency distribution in Example

17 Stem-and-Leaf Display A stem-and-leaf display is a tool that organizes and groups the data while allowing us to see the actual values that make up the data

18 Constructing a Stem-and-Leaf Display To construct a stem-and-leaf display each value is represented with two different groups of digits. The left group of digits is called the stem. The remaining group of digits on the right is called the leaf. There is no rule for the number of digits to be included in the stem. Usually the units digit is the leaf and the remaining digits are the stem

19 Example 5: Constructing a Stemand-Leaf Display The table below indicates the ages of a sample of 20 guests who stayed at Captain Fairfield Inn Bed and Breakfast. Construct a stem-and-leaf display

20 Circle Graphs Circle graphs (also known as pie charts) are often used to compare parts of one or more components of the whole to the whole

21 Example 6: Circus Performances Eight hundred people who attended a Ringling Bros. and Barnum & Bailey Circus were asked to indicate their favorite performance. The circle graph shows the percentage of respondents that answered tigers, elephants, acrobats, jugglers, and other. Determine the number of respondents for each category