- Prepare exercises #8, 9, p. 34 from section 2.3, as well as the review exercise #7, p. 49 from chapter 2.
- Fully interpret the histograms, and write up your work nicely, using a word processor.
- One of these (chosen randomly) will be collected.
- To help you, I distributed a couple of handouts last time:
- Example: heights of NKU students.
- Interpreting a histogram (see p. 29):
- Reminder/warning: the "bin width" can be used to change your impression of a set of data
- Features that describe the shape of a histogram:
- symmetric
- right (positively) skewed
- left (negatively) skewed
- bimodal versus unimodal (e.g. "Old Faithful")
- other(!) -- e.g. multimodal...
(What are some examples that would give rise to skewed distributions?)
- What are the largest and smallest values (range)?
- What are typical values?
- What are central ("average") values?
- What are extreme values?
- Are there unusual, suspicious, or atypical values?
- Creating histograms using StatCrunch and the data from our book.
- Our book used another package -- Minitab -- to do the
statistics. Reference is often made to data sets, e.g.
exam02-04 - To use that data in StatCrunch, you would load the data
from the web, using the name
http://www.nku.edu/~statistics/data/exam02-04.xls - You can also paste in data, if you have it from some other source.
- Our book used another package -- Minitab -- to do the
statistics. Reference is often made to data sets, e.g.
- The interpretation of a histogram should be written up using a
word processer, and should look professional. One of our goals for you
in this course is as follows:
For any assignments or homework exercises that are collected students will create a neatly presented word document. This document will always include:
- Supporting StatCrunch analyses that are copied into the document.
- Well-written, grammatically correct, sentences for any interpretations or explanations.
Examples:
- Example of the interpretation of a histogram (from the sta205 website)
- Here's an interpretation of heights of NKU students.
- Definitions:
- Population: a population is the collection of all the data that
could be observed in a statistical study
- Sample: a sample is a collection of data chosen from the population
of interest.
- Inference: an inference is a decision, estimate, prediction, or generalization about a population based on information contained in a sample from that population.
- Population: a population is the collection of all the data that
could be observed in a statistical study
- Example: Heights of NKU students
- Definitions
- random sample: Consider sampling n
observations from a population. If every collection of n observations
has the same chance of being selected, then the sample is random.
- convenience sampling: If the observations selected
for a sample are those that are easiest to obtain, or are selected because they
are simply available, the sample is haphazard or convenient. (examples, p. 41)
- volunteer sample: If a survey is presented to people in such a way that each individual must take the initiative to reply, the response or opinions form a self-selected or volunteer sample.
- random sample: Consider sampling n
observations from a population. If every collection of n observations
has the same chance of being selected, then the sample is random.
- Example: Heights of NKU students
Measures of central tendency: measures typical (central) values
-
- mean
-
- Also known as the arithmetic average
- center of mass of histogram
- Notation (see p. 64):
- Suppose that you have n data values.
- population (
-- "mu") versus sample means (
-- "xbar")
- sigma (
) notation
- Sensitive to unusual, extreme values
- Let's compute some means....
orange green red yellow blue brown
-
- median
-
- the middle value: insensitive to unusual, extreme values; but not as good as the mean for purposes of statistical inference.
- In the event that there are an even number of data values, the median is the mean of the two values "in the middle".
-
- mode
- the most popular value (or midpoint of the class with largest frequency)
- Relationship between measures of central tendency with skewness of a histogram
- symmetrically uni-modal (a centered hump):
mean and median tend to be the same - skewed right (more extremely large values):
as the mean is sensitive to extremes, it chases the tail to the right. - skewed left (more extremely small values):
as the mean is sensitive to extremes, it chases the tail to the left.
- symmetrically uni-modal (a centered hump):
- Example: Computing mean and median for heights of NKU students, using StatCrunch