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Group Members: Charlie, Tyler,
Renzheng
Model of the
Big Bang
The Big Idea
 Analyze data by using graphs and
numerical summaries
 Use graphs to display categorical or
quantitative data
 Describe the overall pattern by
interpreting shape, center, spread,
and outliers (SOCS)
 Choose a which center and summary
best fits the data. (mean and
deviation or five-number summary)
 Determine the effect of a linear
transformation on center and spread
Vocabulary You Need to Know
 Individuals – are the objects
described by the data. Can be people
or things
 Variables – are any characteristics of
an individual
 Categorical variables - places an
individuals into groups or categories
 Quantitative variables – takes
numerical values like 2 or 4.5
 Distribution – of a variable tells us
what values the variable takes and
how often it takes these values
Key Topics Covered in this Chapter
 Graph categorical data on pie charts
and bar graphs. Graph quantitative
data on stemplots and histograms,
 Ogive or relative cumulative frequency
graphs and timeplots are quantitative
 Describe Shape: symmetric or skewed,
unimodal or no modes
 Describe Center: Mean or Medium.
They are the same in symmetric but in
a skewed, the mean is farther out than
the median near the tail
 Describe Spread: range, quartiles, five
number summary, standard deviation
 Outliers: Median and quartiles are
resistant. Mean and Std deviations arnt
Formulas You Should Know
 Mean
 Variance
 Standard Deviation
 Outliers smaller than Q1 – (1.5 *IQR)
or larger than Q3 – (1.5*IQR)
 Linear transformation xnew = a + bx
(a shifts values up or down, b changes
the size)
 Five number summary (min, Q1,
medium, Q3, max)
 Range = maximum – minimum
Calculator Key Strokes
Enter data into L1 and L2 then
press 1-var stat under calculations.
This will find the mean and
standard deviations.
Remember the difference between
(s) sample and (σ) population
Helpful Hints
 Use back to back stemplots and side by side boxplots are
used to compare quantitative distributions
 Use mean and standard deviation for symmetric and
Normal distributions and the five number summary for
skewed distributions
 The sum of all deviations from their mean will always be
0. s = 0 only when all observations have the same value
 The number n – 1 is called the degrees of freedom of the
variance or std. deviation
 Average value refers to the mean and typical value to the
medium
 Histograms should always have bins of the same size and
the bars touch each other
Example Problem(s)
-799, 0, 4, 32, 54 ,93, 354, 354, 1534, 3942, 4032,
5030
a) Find the Five number summary
b) Find any outliers
c) Find the mean and standard deviation
d) Make a boxplot and a histogram
e) Describe SOCS
a) (-799, 43, 86, 2738, 5030)
b) None
c) Mean = 1219.1666 std dev. = 1965.9759
d)
e) Skewed, no outliers, medium, quartiles