Math 104
February 9, 2005
What’s on the Exam? #1
The closed-book, in-class exam on February 18 covers the following material in the text:
Chapter 3, sections 1, 2, 3, 4 (and related exercises)
Chapter 4, all sections
Chapter 5, all sections
Chapter 7, to the extent necessary
Chapter 8, all sections
Chapter 9, TBD…at most, sections 1, 3, 5.
It does not cover the computer assignments. I’ll try to limit the exam to material we have
covered in class, but I can’t guarantee that absolutely. Calculators are
encouraged. Rulers and extra paper are allowed.
The homework is the best guide for studying. The following checklist is just advisory.
Checklist
Qualitative (labels) vs. quantitative (numerical) variables
Also, for qualitative variables, ordinal vs. nominal
Interpreting histograms…
Given a reasonably well labeled histogram,
Estimate the percentile associated with a particular value.
Estimate the value associated with a particular percentile.
Estimate the percentage of cases in any range of values
If you know the total number of cases, estimate the number of cases in any
bar of the histogram or any range of values
Constructing a histogram…
Understand the “equal area principle” — equal areas in the histograms
should represent equal numbers (or percentages) of observations.
You won’t be required to construct a vertical scale on the exam, but you may
need to do it anyway to get the box heights right.
Describing a distribution…
Unimodal / bimodal / multimodal
Symmetrical / skewed left / skewed right
Outliers
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Measures of “center”…
Given a pile of numbers, be able to compute…
Average (same as mean or “arithmetic mean”)
Median
Mode (if it makes sense for your data)
“RMS” average (square root of the average of the squares)
Any given percentile (Might be called, say, “10th percentile” or
“0.10 percentile)
Q1, Q3 (same as 25th, 75th percentile respectively)
Which measures of center are best for what purposes?
If you add the same number to all values, what happens to the average? Median?
Standard deviation?
If you multiply all of the values by the same number, what happens to the
average? Median? Standard deviation?
Measures of spread…
Given a pile of numbers, be able to compute…
The deviations from the average
SD
IQR ( = interquartile range, same as Q3 – Q1)
If a book or computer program computes a standard deviation that is slightly
larger than yours, is one of you necessarily wrong?
Robust statistics…
What does that mean?
“Average” and “SD” aren’t very robust. Median and IQR are more robust.
Normal distributions…
If a distribution isn’t unimodal and reasonably symmetrical, then it can’t very
well be normal…
Given that your data are normally distributed…
Given average and SD, convert original values to standard units and vice versa
Given average and SD, what fraction of cases are between __ and __ ?
Or, above ___ ?
Or, below ___ ? (OK to use either the book’s method, or the
method we used in class. Both tables will be part of the exam.)
Given average and SD…
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Estimate the value corresponding to a given percentile.
Estimate the percentile corresponding to a given value.
Given some percentiles, have at least a fighting chance to calculate the average
and SD.
Scatterplots…
Given two quantitative (= numerical) variables (for the same list of cases),
construct a scatterplot with one point for each case.
From a scatterplot, estimate the average and SD for each variable separately.
From a scatterplot, be able to guess the correlation coefficient (r).
(At least, be able to recognize the differences between
-0.95, -0.20, 0.00, +0.20, +0.95)
Recognize danger signs…
Cases are really in two or more separate groups
Outliers are present
Describe the relationship between two variables:
Strong or weak?
Positive or negative? (Or too complicated to be either?)
Linear or non-linear?
Construct the “SD line.”
Correlation coefficients…
Given two numerical variables, be able to compute the correlation coefficient (r).
What does it mean for the correlation coefficient to be…
Positive vs. negative?
Small (close to 0) vs. large (close to +1 or -1) ?
Exactly +1 ?
Exactly -1 ?
What happens to r when…
You add the same number to all values of one of the variables
You multiply all values of one variable by the same number
(does it matter if the number is negative?)
Combining subgroup averages…
Given enough information, get an overall average from subgroup averages
or vice versa.
(end, for now)
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