Review for Test 1 Math 1231

1
Review for Test 1Math 1231
This test covers the following chapters Ch
1-6 BRING YOUR LAPTOP!! You should have DataDesk
available to you during the test.
2
Objectives You should

• Be able to identify the Ws (Who, What, Why,
  How, When, Where?) This means.
• If given a description of a dataset
• Be able to identify the WHO (how many of what?)
• Identify the variables measured (the WHAT).
• And the rest of the Ws.

3
More Objectives

• Be able to tell the difference between
  categorical variables and quantitative variables.
• Categorical variable names categories/groups
• Quantitative numbers act as numerical values
• Which graphs do you use for which variables?
• Cat. Var Bar Chart, Pie Chart
• Quant. Var Histogram, dotplot, Stem-and-leaf.
• Remember to READ the Y-axis to distinguish
  between counts/frequencies and percentages.

4
Contingency Tables

• Remember to identify the pool (the Who that were
  interested in)
• Be able to calculate proportions from the table
• Independence Two variables are independent (not
  associated) if the conditional distribution of
  one variable is the same for each category of the
  other.
• Ie, if the of students on probation is the same
  for all GPAs, then GPA and probation are
  independent (not associated).

5
It keeps going

• If I give you a dataset (actual numbers), you
  should be able to
• Make a bar or pie chart in Data Desk
• Make a dotplot or stem-and-leaf plot by hand
• Stem-and-leaf include all stems, even if no
  leaves, and put leaves in ascending order,
  remember to include repeated leaves.
• Make a histogram using DataDesk
• Calculate a proportion/relative frequency from a
  histogram, stem and leaf chart, bar chart, or a
  dataset.

6
And going.

• Given a distribution as data values or histogram
• Describe the shape- potential outliers, number of
  modes, skewness (with direction) or symmetry
• Unimodal, Bimodal, Multimodal, Uniform (flat)
• Symmetric, Skewed to the left, Skewed to the
  right
• Remember that outliers are DEVIATIONS from the
  overall pattern, so they are not generally
  included when deciding symmetry/skewness.
• Be able to identify which distribution from a set
  has a larger spread (only a rough idea)
• Match a verbal distribution description with its
  graphical representation.

7
and going

• Realize that a histogram does not preserve
  individual data values, so you cannot recreate a
  dataset from a histogram.
• Stem and leaf plots DO preserve data values,
  though.
• Think about how real-life distributions would
  look in a histogram (see Ch 4 assigned homework)

8
Histograms and Statistics.

• Given a distribution as data values or histogram
• Use DataDesk to find all measures of center and
  spread.
• Know when to use 5 Summary (skewed dist. or
  outliers) vs. Mean-Standard Deviation (symmetric
  dist)
• Be able to identify which distribution from a set
  has a larger spread

9
Numerical summaries
Measures of Center Midrange (highlow)/2 Media
n Equal AREA point. The value with half the data
above, half below Mean Equal WEIGHT point
(balance pt). Measures of Spread Range
high-low IQR Spread of middle 50 of data
(Q3-Q1) Standard deviation average deviation
from mean.
10
More objectives

• Know what it means if a statistic is resistant
  (not sensitive to outliers- statistic will not
  change much in response to extreme data values)
• Know which statistics are resistant to extreme
  data values, and which are not.
• Median and IQR Resistant
• Mean and SD Somewhat Resistant
• Midrange and Range Not Resistant
• Realize that skewness in a distribution pulls the
  mean away from the median towards the tail.

11
Boxplots

• Be able to use boxplots to compare sets of data
• Graphic representation of 5-Number Summary
• Recognize outliers- pts more than 1.5IQR above Q3
  or below Q1.
• Interpret and compare measure of center and
  spread
• Medians, IQRs, Ranges
• Rough idea of skewness.

12
Z-scores

• Know how to calculate a z-score and what it means
• A z-score represents how many standard deviations
  above or below the mean a data value is
• Provides a common scale for comparison
• (SAT vs ACT, for example)
• (using the Normal
  Model)
• (using statistics from
  data)

13
The Normal Model

• Know what the Normal Model is (unimodal,
  symmetric,
• bell-shaped) N(m,s)
• Know what the Standard Normal Curve is N(0,1)
• Know how to use the 68-95-99.7 Rule
• For approximately normal distributions only
• Estimation, not exact, and remember to use
  symmetry.
• 68 of data within 1 SD of mean, 95 within 2
  SDs, 99.7 within 3 SDs
• Adding a constant to all data values SHIFTS the
  distribution but does not change shape or spread.
• Multiplying each data value by a constant
  multiplies center and spread measures by that
  same constant.

14
Dont Forget
There is a Review of Ch 1-6 in the text. Some
Review problems are available in the text. Make
sure youve gone through ActivStats!
15
Study Suggestions

• If you havent already, DO THE HOMEWORK!
• Review the Graded Homework on MathXL.
• Think about what the big idea is that each
  question is trying to ask.
• Work Practice Test from Website
• Work Suggested problems in the Review in the
  textbook
• Email or IM Dr. Matos with questions, or use
  office hours!