1. Describing Distributions
Section 8.2

2. The unimodal distribution
A standard distribution which occurs naturally in a wide variety of settings. The mean, median and mode are all very close to each other

3. The bimodal distribution
A distribution that usually indicates more than one population being tested
Two modes

4. Positively Skewed Distribution
Typically occurs in populations where there are a large number of positive outliers
Mean is greater than the mode

5. Negatively Skewed Distribution
Typically occurs in populations with a large number of negative outliers.
Mean is less than the mode

6. Try to explain the following:
Why would the reading level of grade 9 students be bimodal?
Why would the marks in a mathematics class be positively skewed?
Why would the marks in a university course be negatively skewed?

7. Experiment: The Reading Level of a Book
The Gunning fog index is one method used to determine the difficulty level of a book.
To calculate the Gunning fog index, find the mean of the number of words per sentence in a passage, and multiply by 0.4
Eg) The Gunning fog index for the first two statements in this slide is:

8. Your task: Determine the reading level of your book
Randomly select 3 paragraphs with at least 5 sentences each
Create a histogram and create a smooth curve over the data to approximate a continuous curve. Classify this data
Calculate the mean, median and mode of the number of words per sentence, and mark these on your histogram
Calculate the standard deviation and variance of the number of words per sentence

9. Distribution for my book

10. Try to write a response to yourself about the following questions:
1. What could the reason be for data to be distributed bimodally?
2. What does a positively skewed distribution tell us?