Histograms

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Histograms

• Lecture 18
• Sec. 4.4.4
• Tue, Feb 17, 2004

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Histograms

• Histogram A display of continuous quantitative
  data in which the data are divided into classes
  and rectangles represent the frequencies of the
  classes.

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Drawing Histograms

• Use Data Set 1 on p. 184.
• Find the maximum value, the minimum value, and
  the range.
• Maximum 51
• Minimum 32
• Range Max Min 51 32 19.

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Drawing Histograms

• Divide the data into classes of equal width.
• The classes must not overlap.
• Choose a convenient starting point.
• Choose a convenient class width.
• Write the endpoints of each class.

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Drawing Histograms

• Starting point 30.
• Class width 5.
• Classes
• 30 up to 35 (but not including 35).
• 35 up to 40.
• 40 up to 45.
• 45 up to 50.
• 50 up to 55.

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Drawing Histograms

• We may denote the classes in either of two ways.
• Interval notation low, high)
• 30, 35),
• 35, 40),
• 40, 45), etc.
• and mean include endpoints.
• ( and ) mean exclude endpoints.

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Drawing Histograms

• Range notation low high
• 30 34,
• 35 39,
• 40 44, etc.
• This notation does not indicate whether the
  endpoints are included.
• Therefore, be sure the endpoints do not overlap.

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Drawing Histograms

• Count the number of observations in each class.
  This is the frequency of the class.

Class Frequency
30, 35) 1
35, 40) 2
40, 45) 8
45, 50) 7
50, 55) 2
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Drawing Histograms

• Draw horizontal and vertical axes.
• On the horizontal axis, show the class
  boundaries.
• On the vertical axis, show uniform reference
  points representing frequencies apropos to the
  data.
• For example, 0, 2, 4,

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Drawing Histograms
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Drawing Histograms

• Over each class, draw a rectangle whose height is
  the frequency of that class.

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Drawing Histograms
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Drawing Histograms
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Drawing Histograms
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Drawing Histograms
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Drawing Histograms
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Drawing Histograms
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Drawing Histograms
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Guidelines

• Never use too few or too many classes.
• Usually 5 to 12 classes is about right.
• Use simple round numbers for the class
  boundaries.
• Mark off the vertical axis uniformly, showing
  regular reference points, not the actual
  frequencies.
• Frequencies must start at 0.

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Lets Do It!

• Lets do it! 4.14, p. 224 Histogram of
  Household Income.
• Lets do it! 4.16, p. 226 Matching Shapes to
  Characteristics.

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Example

• See Example 4.10, p. 227 Histogram versus Bar
  Graph.

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Histograms on the TI-83

• See page 263 for more detailed instructions.
• Enter the data into list L1.
• 45, 41, 51, , 37 ? L1
• Press STAT PLOT
• Turn Plot1 On.
• Select Histogram Type.
• Specify List L1.

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Histograms on the TI-83

• Press WINDOW
• Set Xmin to the starting point.
• Set Xmax to the last endpoint.
• Set Xscl to the class width.
• Set Ymin to 0.
• Set Ymax to the maximum frequency.
• Press GRAPH
• The histogram appears.

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Frequency Distributions on the TI-83

• After getting the histogram, press TRACE.
• The display shows the first class and its
  frequency.
• Use the left arrow to see the other class
  frequencies.

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Assignment

• Page 227 Exercises 30 38.
• Page 249 Exercises 68, 69.