Download - Chapter 1 & 3. Statistics 4 the science of collecting, analyzing, and drawing conclusions from data
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Chapter 1 & 3
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Statisticsthe science of collecting, analyzing, and drawing conclusions from data
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Descriptive statisticsthe methods of organizing & summarizing data
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Inferential statisticsinvolves making generalizations from a sample to a population
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PopulationThe entire collection of individuals or objects about which information is desired
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SampleA subset of the population, selected for study in some prescribed manner
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Variable any characteristic whose value may change from one individual to another
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Dataobservations on single variable or simultaneously on two or more variables
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Types of variables
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Categorical variablesor qualitativeidentifies basic
differentiating characteristics of the population
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Numerical variablesor quantitative observations or measurements
take on numerical valuesmakes sense to average these
valuestwo types - discrete & continuous
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Discrete (numerical)
listable set of valuesusually counts of items
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Continuous (numerical)
data can take on any values in the domain of the variable
usually measurements of something
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Classification by the number of variablesUnivariate - data that describes a single
characteristic of the population
Bivariate - data that describes two characteristics of the population
Multivariate - data that describes more than two characteristics (beyond the scope of this course
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Identify the following variables:1. the income of adults in your city
2. the color of M&M candies selected at random from a bag
3. the number of speeding tickets each student in AP Statistics has received
4. the area code of an individual
5. the birth weights of female babies born at a large hospital over the course of a year
Numerical
Numerical
Numerical
Categorical
Categorical
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Graphs for categorical data
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Bar Graph
Used for categorical data Bars do not touch Categorical variable is typically on the horizontal
axis To describe – comment on which occurred the
most often or least often May make a double bar graph or segmented bar
graph for bivariate categorical data sets
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Using class survey data:
graph birth month
graph gender & handedness
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Pie (Circle) graph
Used for categorical data To make:
– Proportion 360°
– Using a protractor, mark off each part
To describe – comment on which occurred the most often or least often
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Graphs for numerical data
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Dotplot
Used with numerical data (either discrete or continuous)
Made by putting dots (or X’s) on a number line
Can make comparative dotplots by using the same axis for multiple groups
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Distribution Activity . . .
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Types (shapes)of Distributions
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Symmetricalrefers to data in which both sides are
(more or less) the same when the graph is folded vertically down the middle
bell-shaped is a special type
–has a center mound with two sloping tails
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Uniformrefers to data in which every
class has equal or approximately equal frequency
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Skewed (left or right)refers to data in which one
side (tail) is longer than the other side
the direction of skewness is on the side of the longer tail
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Bimodal (multi-modal)refers to data in which two
(or more) classes have the largest frequency & are separated by at least one other class
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How to describe a numerical,
univariate graph
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What strikes you as the most distinctive difference among the distributions of exam scores in classes A, B, & C ?
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1. Centerdiscuss where the middle of
the data fallsthree types of central
tendency–mean, median, & mode
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What strikes you as the most distinctive difference among the distributions of scores in
classes D, E, & F? Class
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2. Spreaddiscuss how spread out the data
isrefers to the variability of the
data–Range, standard deviation, IQR
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What strikes you as the most distinctive difference among the distributions of exam scores in classes G, H, & I ?
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3. Shaperefers to the overall shape of
the distributionsymmetrical, uniform,
skewed, or bimodal
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What strikes you as the most distinctive difference among the distributions of exam scores in class K ?
K
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4. Unusual occurrencesoutliers - value that lies away
from the rest of the datagapsclustersanything else unusual
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5. In contextYou must write your answer
in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!
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More graphs for numerical data
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Stemplots (stem & leaf plots)
Used with univariate, numerical data Must have key so that we know how to read
numbers Can split stems when you have long list of
leaves Can have a comparative stemplot with two
groups
Would a stemplot be a good graph for the number of pieces of gun chewed per day by
AP Stat students? Why or why not?
Would a stemplot be a good graph for the number of pairs of shoes owned by AP Stat
students? Why or why not?
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Example:
The following data are price per ounce for various brands of dandruff shampoo at a local grocery store.
0.32 0.21 0.29 0.54 0.17 0.28 0.36 0.23
Can you make a stemplot with this data?
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Example: Tobacco use in G-rated Movies
Total tobacco exposure time (in seconds) for Disney movies:223 176 548 37 158 51 299 37 11 165 74 9 2 6 23 206 9
Total tobacco exposure time (in seconds) for other studios’ movies:205 162 6 1 117 5 91 155 24 55 17
Make a comparative stemplot.
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Histograms
Used with numerical data Bars touch on histograms Two types
– Discrete• Bars are centered over discrete values
– Continuous• Bars cover a class (interval) of values
For comparative histograms – use two separate graphs with the same scale on the horizontal axis
Would a histogram be a good graph for the fastest speed driven by AP Stat students?
Why or why not?
Would a histogram be a good graph for the number of pieces of gun chewed per day by
AP Stat students? Why or why not?
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Cumulative Relative Frequency Plot(Ogive)
. . . is used to answer questions about percentiles. Percentiles are the percent of individuals that are
at or below a certain value. Quartiles are located every 25% of the data. The
first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2?
Interquartile Range (IQR) is the range of the middle half (50%) of the data.
IQR = Q3 – Q1