Handout 8: Quantitative Data

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Histograms, stem & leaf plots, mean, median, range IQR, symmetry, scatterplots

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16 Terms

1
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What is a histogram?

A graphical display for quantitative data

  • how many bins?

  • where do bins start?

  • start at round number

  • need to label

  • area of all rectangles sum to 1

Don’t make a histogram for categorical variables! (bar/pie charts instead)

<p>A graphical display for quantitative data</p><ul><li><p>how many bins?</p></li><li><p>where do bins start?</p></li><li><p>start at round number</p></li><li><p>need to label</p></li><li><p>area of all rectangles sum to 1</p></li></ul><p>Don’t make a histogram for categorical variables! (bar/pie charts instead)</p><p></p>
2
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What are the type of scales that can be used for the y-axis for histograms?

Frequency = counts

Percent = counts/total counts

Density (total area = 1)

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What are the steps to designing a histogram?

  1. Sort dataset from lowest to highest

  2. Find the range

  3. choose number of bins

  4. find width of bins (1st bin should be a nice number like 10)

  5. Boundaries

  6. Midpoints

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What is a stem & leaf diagram?

A simple way to graphically display quantitative data

  • 1 leaf for every data point → fewer stems

<p>A simple way to graphically display quantitative data</p><ul><li><p>1 leaf for every data point → fewer stems</p></li></ul><p></p>
5
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How do you describe the shape of a histogram?

Describe 3 things: Shape, center, spread

Shape: how many humps/modes?

  • unimodal - 1 peak

  • bimodal - 2 peak

  • multimodal - 3+ peaks

  • uniform - no modes (flat)

<p>Describe 3 things: Shape, center, spread</p><p>Shape: how many humps/modes?</p><ul><li><p>unimodal - 1 peak</p></li><li><p>bimodal - 2 peak</p></li><li><p>multimodal - 3+ peaks</p></li><li><p>uniform - no modes (flat)</p></li></ul><p></p>
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What is symmetry and skew in histograms?

Symmetric: if both sides look roughly similar

Skew: thinner ends of distribution are called tails, if one tail stretches out farther than other it is skewed to the side of the longer tail

  • Left skew (tail to the left)

  • Right skew (tail to the right)

<p>Symmetric: if both sides look roughly similar</p><p>Skew: thinner ends of distribution are called tails, if one tail stretches out farther than other it is skewed to the side of the longer tail</p><ul><li><p>Left skew (tail to the left)</p></li><li><p>Right skew (tail to the right)</p></li></ul><p></p>
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What are odd/unusual features of data/histogram?

Can tell us something interesting about the data

  • Outliers: stand off away from the body of the distribution

  • Gaps

<p>Can tell us something interesting about the data</p><ul><li><p>Outliers: stand off away from the body of the distribution</p></li></ul><ul><li><p>Gaps</p></li></ul><p></p>
8
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What is the median?

The midpoint of the data

  • sort data from smallest to largest → median is value in the middle

  • If the data is even numbered = sum 2 mid values / 2

  • insensitive to extreme values

<p>The midpoint of the data</p><ul><li><p>sort data from smallest to largest → median is value in the middle</p></li><li><p>If the data is even numbered = sum 2 mid values / 2</p></li><li><p>insensitive to extreme values</p></li></ul><p></p>
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What is the mean?

The average value from adding at the values together & dividing the sum by the number of values

  • sensitive to extreme values

<p>The average value from adding at the values together &amp; dividing the sum by the number of values</p><ul><li><p>sensitive to extreme values</p></li></ul><p></p>
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What are maesures of spread (the range)?

Simplest measure of spread is the range

Range = max - min

  • sensitive to outliers

11
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What is the inter-quartile range (IQR)?

IQR = Q3 - Q1

Q1 = lower half of the data (25%)

Q3 = upper half of data (75%)

  • split the data into 2 using the median, find the median of the first half & the median of the second half

  • insensitive to outliers

12
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What is a scatterplot?

Most common & effective display for data → see patterns, trends, relationships

  • best way to check if 2 quantitative variables are related

  • Look for: direction, form, scatter

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What is a linear & non-linear scatterplot?

Linear: If there is a straight line relationship

Non-linear: if there is curvature

<p>Linear: If there is a straight line relationship</p><p>Non-linear: if there is curvature</p>
14
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What is a tight relationship vs. no pattern scatterplot?

Tight: points appear to follow single linear relationship

  • extreme: all data falls on a line (± 1 corr coeff)

No pattern: points appear vague cloud with no trend

  • corr coeff = 0

<p>Tight: points appear to follow single linear relationship</p><ul><li><p>extreme: all data falls on a line (<span>± 1 corr coeff)</span></p></li></ul><p>No pattern: points appear vague cloud with no trend</p><ul><li><p>corr coeff = 0</p></li></ul><p></p><p></p>
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What is a negative or positive scatter plot?

Negative: pattern runs in negative linear direction → substitute goods

Positive: trend runs in positive linear direction → complementary goods

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What kind of variables go on the x & y axes?

X-axis: the explanatory/predictor variable (independent variable)

Y-axis: the reponse variable (dependent variable)