# Stats

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1. individuals
• Individuals can be people,
• animals, plants, or any object of interest.
2. variable
• any characteristic of an
• individual. A variable varies
• among individuals.
3. distribution
• tells us what values the
• variable takes and how often it takes these values.
4. quantitative variable
• Something that takes
• numerical values for which arithmetic operations, such as adding and averaging,
• make sense.
5. categorical variable
• Something that falls into
• one of several categories. What can be counted is the count or proportion of
• individuals in each category
6. Ways to chart categorical data
Bar graphs and pie charts
7. Bar graphs
• Each category is
• represented by one bar. The bar’s height shows the count (or sometimes the
• percentage) for that particular category
8. Pie charts
• Each slice represents a piece of one whole. The size of
• a slice depends on what percent of the whole this category represents.
9. Ways to chart quantitative data
Histograms and stemplots, and Line graphs: time plots
10. Line graphs: time plots
• Use when there is a
• meaningful sequence, like time. The line connecting the points helps emphasize
• any change over time
11. Histograms and stemplots
• These are summary graphs
• for a single variable. They are very useful to understand the pattern of
• variability in the data
12. Histograms
• - The range of values that a
• variable can take is divided into equal size intervals.
• - The histogram shows the
• number of individual data points that fall in each interval.
13. stem plots
• -To compare two related distributions, a back-to-back stem plot with common
• stems is useful.
• -Stem plots do not work well for large
• datasets.
• -When the observed values have too many
• digits, trim the numbers before making
• a stem plot.
• -When plotting a moderate number of
• observations, you can split each
• stem.
14. Interpreting histograms
We can describe the overall pattern of a histogram by its shape, center, and spread.
15. A distribution is symmetric if ...
• the right and left sides
• of the histogram are approximately mirror images of each other.
16. A distribution is skewed to the right
• if the right side of
• the histogram (side with larger values) extends much farther out than the left
• side
17. skewed to the left
• if the left side of
• the histogram extends much farther out than the right side
18. An important kind of
deviation is an outlier
• Outliers are observations that lie outside the overall
• pattern of a distribution
19. A trend is
a rise or fall that persists over time, despite small irregularities.
20. seasonal variation
A pattern that repeats itself at regular intervals of time
21. mean
• add all values, then divide by the number of individuals. It is the “center of
• mass.”
22. median
• the midpoint of a
• distribution—the number such that half of the observations are smaller and half are larger
23. Comparing the mean and the median
• The
• mean and the median are the same only if the distribution is symmetrical. The
• median is a measure of center that is resistant to skew and outliers. The mean
• is not
24. first quartile, Q1
• the value
• in the sample that has 25% of the data at or below it
25. third quartile, Q3
• is the
• value in the sample that has 75% of the data at or below it
26. “1.5 * IQR rule for outliers
• if it falls more than 1.5
• times the size of the interquartile range (IQR) above the first quartile or
• below the third quartile
27. variance s2.
﻿
28. standard
deviation s.
• used only when the mean is the measure of center.
• -s = 0 only when all observations have the same
• value and there is no spread.
• Otherwise, s > 0.
• -s is not resistant to outliers.
• -s has the same units of measurement as the
• original observations.
29. linear transformation
• do not change the basic shape of a distribution (skew, symmetry,
• multimodal). But they do change the measures of center and spread:
30. density curve
• The
• total area under the curve, by definition, is equal to 1, or 100%.

• The area under the
• curve for a range of values is the proportion of all observations for that
• range
31. median of a density curve is
the equal-areas point
• the
• point that divides the area under the curve in half.
32. mean of a density curve is
the balance point
at which the curve would balance if it were made of solid material.
33. Normal – or Gaussian –
distributions
• a family of symmetrical,
• bell-shaped density curves defined by a mean m (mu) and a standard deviation
• s (sigma) : N(m,s).
34. z-score
• measures the number of standard deviations that a data value x
• is from the mean m.
 Author: Anonymous ID: 6102 Card Set: Stats Updated: 2010-02-05 07:21:20 Tags: stats ch 1 Folders: Description: Stats Chapter 1 Show Answers: