Section 2.3 Histograms and Frequency Distributions

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Section 2.3Histograms and Frequency Distributions

• Chapter 2

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Histogram

• Looks like a bar graph but differs in 2 ways
• The bars always touch.
• The width of the bar represents a quantitative
  value range.
• Used to summarize large sets of data.
• Can tell how many are in each group, but not how
  many are a particular value.
• Histograms must include a title and scaled
  labeled horizontal and vertical scales.

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Making a Histogram

• Each bar represents a class. Decide how many
  classes you want. (Usually 5-15)
• Calculate the class width
• Increase this number to the next whole number.
• List the class limits in a frequency table.
• Tally the how many numbers are in each class.
  List in the frequency table.
• NOTE If a data value falls on a class limit, it
  goes with the higher class.

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Making a Histogram Cont.

• Draw the horizontal axis.
• Start on the left side of the axis and label it
  with the smallest class limit.
• Continuing labeling with each class limit.
• Draw and label the vertical axis with the
  frequency.
• Draw your bars.
• Title your graph.
• EX p.59 3

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Using Relative Frequency

• Relative frequencies are the frequencies written
  as a percentage.
• Take the frequency for each class and divide it
  by the total number of data values.
• Add a 3rd column for this in your frequency
  table.
• You can make a relative frequency histogram by
  using relative frequency on the vertical axis
  instead of frequency.
• Lets add to our previous example.

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Using Cumulative Frequencies

• A cumulative frequency is the sum of all of the
  frequencies to that point.
• Add a 3rd column for this in your frequency
  table.
• You can make a cumulative frequency histogram by
  using cumulative frequency on the vertical axis
  instead of frequency.
• Used to determine how many values are above OR
  below a set amount.
• Lets add to our previous example.

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Distribution of Data

• Histograms help us determine how the data is
  distributed.
• If your data is a from a good random sample, the
  distribution shape of the sample data should be
  similar to the actual distribution shape for the
  entire population.

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Distribution Shapes

• Symmetrical
• Looks like a mound or a bell
• Uniform (aka Rectangular)
• Looks like a rectangle
• Skewed Left
• The long tail is on the left (mound on right)
• Skewed Right
• The long tail is on the right (mound on left)
• Bimodal
• Two mounds