The Dot Plot

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The Dot Plot

• What is it? How to Draw it
• Bet youve never seen a graph like this one
  before. . .

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What is a Dot Plot?

• A dot plot is a graph that shows the
  distribution of a quantitative variable above a
  number line with small periods, dots, circles or
  xs. It plots a quantitative variable against a
  quantitative variable.
• Axes on a dot plot
• A dot plot only has an x-axis.
• The y-axis is never drawn
• Advantage of a dot plot
• Moderate amounts of quantitative data can be
  quickly visualized

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What is a Dot Plot?

• 2 Variables on a dot plot
• x-axis variable is quantitative and identified
• y-axis variable is implied since the y-axis is
  never drawn.
• y-axis variable is the count and so is
  normally discrete quantitative

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Making a Dot Plot

• I want to know more about my students who take
  Intro Stats so Ive decided to take a survey and
  make a dot plot of the results
• Id like to find out about the pets they have in
  their household.
• The question then becomes
• How many pets are in your household?

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Making a Dot Plot from Live Data
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Dot Plot Example
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Freq Table Example 4 Classes Combined
Mean 2.52 pets Median 2 pets Mode 0 pets
(37x) Range 30 pets Spread 0 - 30 pets n
134 students
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Dot Plot Example 4 Classes Combined
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Dot Plot Statistical Vocabulary Background

• Spread (also called Variability)
• The spread of data in statistics is the smallest
  value in a data set and the largest value
• It is always expressed as 2 numbers
• Prefer to write smallest then largest number
• Units are important
• Range
• The range of data in statistics is the
  difference between the smallest value and the
  largest value
• Take the spread and subtract the two numbers
  large small
• Units are important

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Dot Plot Statistical Vocabulary Background

• One Measure of Center
• One measure of the center of a data distribution
  is the median, the place where the data tends to
  be ½ above and ½ below.
• Units are important
• Mode
• The mode of data is a place or places with the
  largest number of data with the same value. Units
  are important.

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Dot Plot How to Describe It

• Shape
• The shape of a data distribution possibilities
• 1) Symmetry
• Symmetric Also Fairly Symmetrical
• Skewed Left (negatively skewed)
• Skewed Right (positively skewed)
• 2) Peaks
• Single Peaked (unimodal)
• Double Peaked (bimodal)
• Multi Peaked (multimodal)
• NOTE Data have modes, dot plots have peaks

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Student Scores in Andersons Cr Writing
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Student Scores in Andersons Cr Writing
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of Population Over 65
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Population over 65 Data Sorted by
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Make Dot Plot of State Population Data
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Dot Plot How to Describe It

• More on Shape
• Symmetric
• When the left right sides of a distribution
  are mirror images of one another
• Fairly Symmetric
• When the left and right sides of a distribution
  are almost mirror images of one another, but
  there are small exceptions.
• Skewed Left (negatively skewed)
• If a distribution extends much farther out to
  the left. The direction of skewness is on the
  side of the longer tail, in this case LEFT.
• Skewed Right (positively skewed)
• If a distribution extends much farther out to
  the right. The direction of skewness is on the
  side of the longer tail, in this case RIGHT.

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Dot Plot What it Looks Like

• Shape Symmetry
• Symmetric

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Dot Plot What it Looks Like

• More on Shape Non Symmetric
• Skewed Left (negatively skewed)
• Skewed Right (positively skewed)

tail
tail
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Goals by US Womens Soccer
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Goals by US Womens SoccerOrdered Ascending
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Dot Plot of Goals by US Womens Soccer
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Living in Poverty East of the Mississippi
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Living in Poverty East of the MississippiOrdered
Ascending
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Living in Poverty East of the Mississippi
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Dot Plot Mean Median Essentials

• Skew on a dot plot in relation to mean and median
• Youve drawn the line that connects the dot plot
  points on the top of the distribution. The line
  clearly shows right or left skew.
• If you have right skew, the mean will be to the
  right of (greater than) the median, as the mean
  follows the tail of the distribution.

median
mean
tail
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Dot Plot Mean Median Essentials

• Skew on a dot plot in relation to mean and median
• If you have left skew, the mean will be to the
  left of (less than) the median, as the mean
  follows the tail of the distribution.

median
mean
tail
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Dot Plot Describing Peaks

• Peaks
• Unimodal
• Bimodal

Multimodal (3 or more peaks)
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TI83 and Sort Ascending

• How to Sort Data in Ascending Order
• Enter all values in a list at STAT EDIT
• Exit to Home Screen using 2nd MODE
• Hit STAT key. Go to 2 SORT A(. Hit ENTER
• Type 2nd 1 (if the data is in List 1). Hit Enter
• Done appears
• Check your data in List 1. It should be sorted.
• Use your eyes to find the range spread from
  the sorted list.

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Dot Plot TI Essentials

• Finding Mean and Median
• Enter your data as a list in STAT EDIT
• Exit to home screen 2nd Mode
• Go to 2nd STAT.
• Right Arrow to MATH
• 3 is Mean hit Enter type 2nd and list
  Enter
• 4 is Median hit Enter type 2nd and list
• Enter
• Calculator does not give Mode. You need your
  eyes for that

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Glucose Blood Levels

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Glucose Blood Levels

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WBNA EAST Free ThrowsData in Ascending Order
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WBNA Free ThrowsDot Plot
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Dot Plot How to Describe It

• Unusual Features. Possibilities include--
• Potential Outliers any data value that falls
  out of the
• pattern of the rest of the distribution. A
  potential outlier will lie at either extreme of
  the data when it is written in order. (We will
  learn how to calculate actual outliers later.
  For now, we will call these points potential
  outliers)
• Clusters isolated groups of values. Clusters
  begin when frequency gt1 and end before frequency
  returns to 1 or zero.
• Gaps large spaces between values. Write gap
  values from beginning empty space to end empty
  space. A gap of one number is NOT a gap.

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Fuel ConsumptionData
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Fuel ConsumptionDot Plot