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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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