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Chapter 1

Introduction to the Practise of Statistics - Chapter 1

8 Pages
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Department
Statistics
Course Code
STAB22H3
Professor
Moras

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Introduction to the Practise of Statistics
Introduction
- Statistics: The science of learning from data (numerical facts)
- Context of data includes understanding variables that are recorded with special
instruments
- Individuals: Objects described in a set of data (sometimes people but when they are not,
they are cases)
- Variables: Any characteristics of an individual, can take different values for different
individuals, 2 types:
Categorical: Places individual into 1 or >2 groups/categories (i.e. sex = female or
male)
Quantitative: Takes numerical values of which arithmetic co operations such as
adding or averaging take place
Distribution of a variable tells us what values it takes and how often it takes these
values
1.1 Displaying Distributions with Graphs
- Exploratory Data Analysis: Using statistical tools and ideas to examine data in order to
describe main features, 2 basic strategies:
Begin by examining each variable move on to study relationships among
variables
Begin with a graph(s) add numerical summaries of specific aspects of data
- Categorical Variables:
Distribution of categorical variables list the categories and give the cont/percent of
individuals that all in each category
Graphs to Represent Variables:
A.Bar Graphs
B.Pie Chart: Require that you include all categories that make a WHOLE use only
when you want to emphasize each categorys relation to the whole
- Quantitative Variables:
www.notesolution.com
Graphs to Represent Variables:
A.Histogram: Bars broken into sub-intervals (bins), breaks range of variable into
classes and displays only the count of percent of observations that fall into each class
X-axis covers RANGE into data
Can learn the shape of distribution ( i.e. bell shape, skew / , unimodal)
Extreme values of distribution are in the tails of the distribution
See distribution (visual inspection)
3 types of histograms
1.Frequency: Height/count (i.e. # of individuals that move mpg in bin)
2. Relative Frequency: Height of bat/bin if the # of individuals that fall into
that bin
3.Density: Area of the bar/bin is the # of individuals in the data set that fill
into that bin
Examples: Distribution of IQ Scores:
1.Divide the range of data into classes of equal width. The score ranges is from
81-145.
2.Count the # of individual sin each class counts are called frequency, and
the table to frequencies of all classes is frequency table
3.Draw histogram
B.Stem Plot/ Stem-And-Leaf Plot: Gives interpretation of shape of distribution
while including the actual numerical values in the graph, works best for small
numbers of observations that are all >0
How to make a Stemplot:
1.Separates each observation into stem (most digit) and leaf (final digit)
stems may have as many digits as needed but each leaf contains only 1 digit
2.Write stems in vertical column with the smallest at the top and draw | at the
of the column
3.Write each leaf in the row to the of its stem (optional, in increasing order)
Stemplots do NOT work well for LARGE DATA SETS, where ach stem must hold
large # of leave 2 modifications to distribute observations:
www.notesolution.com
1.Splitting each stem into 2: One with leaves 0-4 and another with 5-9
2.Truncating (round DOWN)/ Removing the # by removing the last digit(s)
before making the stem plot
- Examining Distributions:
In any graph of data, look for the overall pattern and for striking deviations from
that pattern
You can describe the overall pattern of distribution by it shape, center and spread
An important kind of deviation is an outlier (individual value that falls outside overall
pattern)
Does the distribution have 1 or more major peaks (modes)? 1 peak is called unimodal.
A distribution is symmetric if values smaller and larger than midpoint are mirror
images. It is skewed to the right if the right tail (larger values) and longer than the
left tail (smaller values)
- Time Plots: A time plot of a variable plots each observation against time at which it was
measured. Time is on the horizontal scale and the variable is on the vertical scale.
Connecting the data point by lines helps emphasize any change over time.
Sometimes there is a trend (persistent, long term rise or fall)that is shown
A pattern in a time series that repeats itself at known regular intervals of time is called
seasonal variation. Because of seasonal variation, agencies often adjust to this
(seasonally adjusted) to help avoid misrepresentation.
Many interesting data sets are time series (measurements of a variable taken at
regular intervals over time)
1.2 Describing Distributions with Numbers
- Measuring Center: The Mean The average value
To find the mean of a set of observations, add their values and divide by the number of
observations
www.notesolution.com

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Description
Introduction to the Practise of Statistics Introduction - Statistics: The science of learning from data (numerical facts) - Context of data includes understanding variables that are recorded with special instruments - Individuals: Objects described in a set of data (sometimes people but when they are not, they are cases) - Variables: Any characteristics of an individual, can take different values for different individuals, 2 types: Categorical: Places individual into 1 or >2 groupscategories (i.e. sex = female or male) Quantitative: Takes numerical values of which arithmetic co operations such as adding or averaging take place Distribution of a variable tells us what values it takes and how often it takes these values 1.1 Displaying Distributions with Graphs - Exploratory Data Analysis: Using statistical tools and ideas to examine data in order to describe main features, 2 basic strategies: Begin by examining each variable move on to study relationships among variables Begin with a graph(s) add numerical summaries of specific aspects of data - Categorical Variables: Distribution of categorical variables list the categories and give the contpercent of individuals that all in each category Graphs to Represent Variables: A. Bar Graphs B. Pie Chart: Require that you include all categories that make a WHOLE use only when you want to emphasize each categorys relation to the whole - Quantitative Variables: www.notesolution.com
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