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Exploring Data
Describing Distributions
Graphically
Histograms
Histograms are similar to stemplots
They break data into intervals so that you can
determine the center, shape and spread of the
distribution
Unlike stemplots, each individual data point is
not included in the histogram only represented
in its interval
Constructing a Histogram
Step 1 – Divide the data into bins (intervals) of equal
width. Be sure the data will fit into these as nicely as
possible
Step 2 – Create a frequency table, listing each interval
and the count of the number of data in each interval
Step 3 – Title and scale your graph and label your axes
appropriately (Bins on x-axis, frequencies on y-axis)
Step 4 – Graph your histogram. Be sure you DO NOT
leave spaces between the bars unless there is an empty
bin
Patterns in Histograms
• Center –
• Is it skewed? If there is a tail on either side
that is longer than the other the side the tail is
on is considered to be skewed (think skewer)
• Right skew has a few large values, but most
values are small
• Left skew has a few small values, but most
values are large
More Patterns
• Shape
Does it have one peak (unimodal)?
Does it have two peaks (bimodal)?
Is it symmetric?
Is it roughly symmetric?
Deviations
• Spread
Are there any outliers (numbers by
themselves)?
Are there any deviations from symmetry?
What is the range of values that are being
displayed?

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Exploring data histograms

  • 2. Histograms Histograms are similar to stemplots They break data into intervals so that you can determine the center, shape and spread of the distribution Unlike stemplots, each individual data point is not included in the histogram only represented in its interval
  • 3. Constructing a Histogram Step 1 – Divide the data into bins (intervals) of equal width. Be sure the data will fit into these as nicely as possible Step 2 – Create a frequency table, listing each interval and the count of the number of data in each interval Step 3 – Title and scale your graph and label your axes appropriately (Bins on x-axis, frequencies on y-axis) Step 4 – Graph your histogram. Be sure you DO NOT leave spaces between the bars unless there is an empty bin
  • 4. Patterns in Histograms • Center – • Is it skewed? If there is a tail on either side that is longer than the other the side the tail is on is considered to be skewed (think skewer) • Right skew has a few large values, but most values are small • Left skew has a few small values, but most values are large
  • 5. More Patterns • Shape Does it have one peak (unimodal)? Does it have two peaks (bimodal)? Is it symmetric? Is it roughly symmetric?
  • 6. Deviations • Spread Are there any outliers (numbers by themselves)? Are there any deviations from symmetry? What is the range of values that are being displayed?