Dot plots continued

1
Dot plots continued

• We can use a dot plot to detect
• Clusters
• Groups
• Outliers

• Also if the sample size is small enough we can
  attach labels
• Dotplots are used when the sample size is small
  to moderate (n ? 20)

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Distribution of a quantitative variable

• The pattern of variation of a variable is called
  its distribution.
• The distribution of a quantitative variable
  records its numerical values and how often each
  value occurs.
• Stem and leaf plots
• A stem and leaf plot is a simple tool for examing
  the distribution of a quantitative variable
• Stem and leaf plots (sometimes called stemplots)
  are good when we have a small data set, and all
  of the values are greater than zero.

3
Making a stem and leaf plot

• Separate each observation into a stem consisting
  of all but the final (rightmost) digit and a leaf
  containing the final digit. Stems may consist of
  as many digits as needed, but each leaf contains
  only a single digit.
• Write the stems in a vertical column with the
  smallest at the top and the largest at the
  bottom, and draw a vertical line at the right of
  this column
• Write each leaf in the row to the right of its
  stem, in increasing order out from the stem
• NB the last step is easier if the data are
  sorted

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Example

• The following digits represent the speeds (in
  km/hr) of 11 motorists caught speeding by a speed
  camera
• 120, 114, 122, 118, 123, 110, 123, 110, 127,
  125, 112
• Create a stem and leaf plot of this data.
• Sort the data
• 110, 110, 112, 114, 118, 120, 122, 123, 123,
  125, 127
• Now we can see there are two stems 11 and 12

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Exercise

• Construct a stem and leaf plot for the
  cholesterol data

142 160 186 206 210 220 224
226 234 236 236 242 244 266 270
272 276 278 280 280 282 282
288 288 294 310 318 360
6
Histograms

• Most of us are familiar with histograms
• In a histogram, we use bars (rectangles) to
  represent the relative frequency of a particular
  data item or range of values
• As with a stem and leaf plot, the hardest part is
  choosing the class intervals the equivalent of
  the stems
• Pick out the minimum and maximum values
• Choose a convenient number of equal sized class
  intervals which contain the minimum and the
  maximum
• Above each class interval draw a rectangle with
  its height equal to the number of observations
  falling into that interval

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Traffic accident death rates (per 100,000 of pop)
for 30 countries
8
Frequency table for traffic-deaths data

• Class Interval Tally Frequency
• 5 10- 2
• 10 15- 15
• 20- 7
• - 25- 4
• - 30- 2
• Total 30

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Stem and leaf plots in Minitab

• Click on Graph gt Stem and Leaf Plot.
• Enter the column name of your data into the
  Variables box
• Click OK

Character Stem-and-Leaf Display Stem-and-leaf
of Choleste N 28 Leaf Unit 10 1 1
4 2 1 6 3 1 8 5 2 01 11
2 222333 13 2 44 (5) 2 67777 10
2 8888889 3 3 11 1 3 1 3
1 3 6
Shows cumulative counts from each end
Group in which the median is
Note the rounding
11
Summary

• Stem and leaf plots are good for getting an idea
  of the distribution of a small data set (less
  than 20 observations)
• The choice of stem is subjective and will affect
  the shape of the plot
• Use rounding if it helps
• Minitab can do stem and leaf plots, Excel cannot
• For bigger data sets (gt20) histograms are a good
  way of displaying the data
• Minitab can create a histogram for you (Graph gt
  Histogram)
• Excel can create histograms but needs a little
  help