Histograms are used to graphically represent the distribution of data by dividing it into intervals and counting the frequency of data points within each interval. To construct a histogram, the data is divided into bins of equal width and a frequency table is made listing the count in each bin. The bins are then graphed on the x-axis with their corresponding frequencies on the y-axis. Patterns in histograms can reveal the center, shape, spread and skewness of the distribution through characteristics like peaks, symmetry, outliers and the range of values.

1. Exploring Data
Describing Distributions
Graphically

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?