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Chapter 5

73-100 Chapter 5: Intro to Data Analysis - Textbook + Lecture notes - ch. 5
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Department
Business
Course Code
73-100
Professor
Peter Miller

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CHAPTER 5 Displaying and Describing Quantitative Data
1. Distribution – gives the possible values of a variable and the frequency or relative frequency
of each value
Histogram – plots the bin counts (number of cases that fall into each bin) as the heights of bars
(!! bar chart!)
- No gaps between bars (unless there are actual gaps in the data - important to note)
- Bin width is important to make data clear
- When value is between bins, put it in the higher bin (ex. for $0-$5 ($4.99) and $5-$10,
the $5 goes in 2nd bin)
- Imagine what the distribution might look like before making it – can spot errors easier
- Relative frequency histogram – faithful to the area principle by displaying percentage of
cases in each bin instead of the count
Stem-and-Leaf Displays – like histograms, but also give individual values
- Stem: base part of each number (ex. from $2.32, stem is 2)
- Leaf: next digit (rounded) in number (ex. from $2.32, leaf is 3)
- Add multiple leafs behind each stem
- Ex. 2 | 3 7 8 or 3 | 5
- Each digit should be same width (to satisfy the area principle)
- Great for quick pencil and paper diagrams
Quantitative Data Condition – the data are values of a quantitative variable whose units are
known
2. Shape of a distribution - describes in terms of its modes (single x multiple), symmetry
(symmetric x skewed) and whether it has any gaps or outlying values
- Mode – single, central bump (peak) or several, separated bumps
- Unimodal – histograms having one central bump (mode)
- Bimodal – histograms with two humps (modes) – indication of 2 group in the data
(should investigate further)
- Multimodal – histograms with more 3+ modes
- Uniform – distribution whose histogram doesn’t appear to have any mode, all bars are
approx. the same height
- Symmetry – if the halves on either side of the centre look (approx.) like mirror images
- Tails – usually thinner ends of the distribution
- Skewed tail – when one tails is stretched out farther than the other (skewed to side of
longer tail)
- Outliers – stragglers that stand off away from the body of the distribution
- Always be on the lookout for these abnormalities
- Can be very informative part of data, or an error
Uniform – a distribution that’s roughly flat
3. Centre – middle of a distribution (usually summarized numerically by the mean or median)
- Average of data – calculation to get precise middle:
- Mean of y - Add all values of the variable, y, and divide that sum (total) by the number of
data values, n (**only used for symmetric data) 𝑦=!"#$%!
!
=!!!
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Description
CHAPTER 5 Displaying and Describing Quantitative Data 1. Distribution gives the possible values of a variable and the frequency or relative frequency of each value Histogram plots the bin counts (number of cases that fall into each bin) as the heights of bars (!! bar chart!) No gaps between bars (unless there are actual gaps in the data important to note) Bin width is important to make data clear When value is betwndn bins, put it in the higher bin (ex. for 05 (4.99) and 510, the 5 goes in 2 bin) Imagine what the distribution might look like before making it can spot errors easier Relative frequency histogram faithful to the area principle by displaying percentage of cases in each bin instead of the count StemandLeaf Displays like histograms, but also give individual values Stem: base part of each number (ex. from 2.32, stem is 2) Leaf: next digit (rounded) in number (ex. from 2.32, leaf is 3) Add multiple leafs behind each stem Ex. 2 3 7 8 or 3 5 Each digit should be same width (to satisfy the area principle) Great for quick pencil and paper diagrams Quantitative Data Condition the data are values of a quantitative variable whose units are known 2. Shape of a distribution describes in terms of its modes (single x multiple), symmetry (symmetric x skewed) and whether it has any gaps or outlying values Mode single, central bump (peak) or several, separated bumps Unimodal histograms having one central bump (mode) Bimodal histograms with two humps (modes) indication of 2 group in the data (should investigate further) Multimodal histograms with more 3+ modes Uniform distribution whose histogram doesnt appear to have any mode, all bars are approx. the same height Symmetry if the halves on either side of the centre look (approx.) like mirror images Tails usually thinner ends of the distribution Skewed tail when one tails is stretched out farther than the other (skewed to side of longer tail) Outliers stragglers that stand off away from the body of the distribution Always be on the lookout for these abnormalities Can be very informative part of data, or an error Uniform a distribution thats roughly flat 3. Centre middle of a distribution (usually summarized numerically by the mean or median) Average of data calculation to get precise middle: Mean of y Add all values of the variable, y, and divide that sum (total) by the number of data values, n (**only used for symmetric data) = =
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