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Chapter 5

73-100 Chapter Notes - Chapter 5: Time Series, Bar Chart, Squared Deviations From The MeanPremium

4 pages57 viewsWinter 2018

Course Code
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 $2.32, leaf is 3)
- Add multiple leafs behind each stem
- Ex. 2 | 3 7 8 or 3 | 5
- Each digit should be same width (to satisfy the area principle)
- Great for quick pencil and paper diagrams
Quantitative Data Condition – the data are values of a quantitative variable whose units are
2. Shape of a distribution - describes in terms of its modes (single x multiple), symmetry
(symmetric x skewed) and whether it has any gaps or outlying values
- Mode – single, central bump (peak) or several, separated bumps
- Unimodal – histograms having one central bump (mode)
- Bimodal – histograms with two humps (modes) – indication of 2 group in the data
(should investigate further)
- Multimodal – histograms with more 3+ modes
- Uniform – distribution whose histogram doesn’t appear to have any mode, all bars are
approx. the same height
- Symmetry – if the halves on either side of the centre look (approx.) like mirror images
- Tails – usually thinner ends of the distribution
- Skewed tail – when one tails is stretched out farther than the other (skewed to side of
longer tail)
- Outliers – stragglers that stand off away from the body of the distribution
- Always be on the lookout for these abnormalities
- Can be very informative part of data, or an error
Uniform – a distribution that’s roughly flat
3. Centre – middle of a distribution (usually summarized numerically by the mean or median)
- Average of data – calculation to get precise middle:
- Mean of y - Add all values of the variable, y, and divide that sum (total) by the number of
data values, n (**only used for symmetric data) 𝑦=!"#$%!
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