DIS - Statistical Graphs Lesson
Statistical Graphs
Dealing with Data
In order to deal with data, we need ways of organizing it. In past courses, you have learned several ways to do that: dot plots, stem and leaf plots, histograms, box plots and others. We will review histograms here.
To create a histogram, unless you have a small data set, you first need to make a frequency table. Let's look at the following example below:
Make a histogram for the following sets of numbers: 10, 12, 12, 13, 14, 11, 10, 13, 15, 14
Here is the frequency table and histogram for the data above: (technically, in a histogram, the bars should have No Spaces in between them)
|
Number |
Count |
Histogram |
|---|---|---|
|
10 |
2 |
|
|
11 |
1 |
|
|
12 |
2 |
|
|
13 |
2 |
|
|
14 |
2 |
|
|
15 |
1 |
For a discrete random variable a histogram should have a separate bar for each possible value. However, if you have a very large number of possible values you can make a frequency table for the intervals. Each interval should be the same width. This may occur if you are making a histogram for the scores on an exam. Since they range from 0 to 100, you can have the width of each interval be 10.
Here are the general steps to create a histogram:
- Divide the range of data into intervals of equal width. For a discrete random variable with few values, use the actual values.
- Count the number of observations in each interval, forming a frequency table.
- On the horizontal axis, label the values or endpoints of each interval. Draw a bar over each interval with height equal to its frequency indicated on the vertical axis.
Random, Discrete, and Categorical Variables
Watch the following video on identifying individuals and random variables in a data set.
Video 1 introduces random variables.
In video 2, an example is shown that explains differences between individual items and individual items as categorical variables.
Video 3 introduces discrete and continuous random variables.
Data Distributions with Dot Plots, Stem-and-Leaf Plots, and Frequency Tables
Watch the following videos exploring dot plots, stem and leaf plots, and frequency tables.
In video 1, an example is shown that computes the mean, median, and mode of a set of data.
Video 2 gives four examples of creating and reading stem-and-leaf plots.
Video 3 compares the distributions of data sets from two dot plots.
Box-and-Whisker Plots - Exploration
In this video, from the beginning to 8:24, there are three examples (numbered 1a, 1b, and 1c) of creating box-and-whisker plots from a set of data. From 8:25 to 13:42, two examples are shown where data is computed from box-and-whisker plots. From 13:43 to the end of the video, an example is shown that creates the various data needed to complete a box-and-whisker plot.
Frequency Tables and Histograms - Exploration
In the first 10:20 of this video, an example with four parts is shown that explores frequency tables and then creates frequency histograms. From 10:21 to the end of the video, an example is shown where the range, width, and interval notation for a frequency table or histogram.
Histograms - Exploration
Watch the following videos exploring Histograms.
In video 1, an example is given that shows how to create a histogram.
In video 2, an example is given that shows how to interpret a frequency distribution.
Representation of Data Sets - Exploration (Videos 1 and 2)
Watch the following videos to explore the various representations of data sets.
In the first 5:12 of video 1, an example in three parts is shown that computes the mean, median, and mode from dot plots. From 5:13 to the end of the video, two examples are shown where data is gathered from a frequency distribution, and where a frequency distribution is created.
In video 2, an example is shown that creates a frequency distribution and a dot plot from a data set.
Symmetry, Skewness, Modalities of Graphs - Exploration (Videos 1 and 2)
Watch the following videos exploring various aspects of statistical graphs.
In the first 6:54 of video 1, two examples are shown how to compute the mean and standard deviation of two histograms. From 6:55 to the end of the video an example with five parts is shown that deals with types of distributions of the histograms: symmetry, skewed right, skewed left, bi-modal, and uniform.
In video 2, an example that explores conclusions drawn from dot plots and histograms. These dot plots and histograms show examples of symmetry, skewed right, skewed left, bi-modal, and uniform.
Graphs of Data Presentation
IMAGES CREATED BY GAVS