Dotplots & Stemplots (College Board AP® Statistics)

Dotplots

What is a dotplot?

• A dotplot is a chart that counts the frequency of data values using dots or crosses

• Dotplots are usually used for discrete data, where dots of identical values are stacked vertically on top of each other

  • They can be used for either categorical data (data in categories), e.g. colours

  • or quantitative data (numerical data), e.g. age

• If dotplots are used for continuous data

  • then stacked dots represent nearly identical values

  • e.g. a dot at could be any value in the interval

How do I interpret dotplots?

• The dotplot above shows the number of pets owned by 15 students

  • 3 students have no pets, 2 students have 1 pet, 6 students have 2 pets, etc.

Can I use dotplots to comment on the shape of the distribution?

• Dotplots are a good way to see the shape of the distribution of the data

• You can comment on skew or symmetry for quantitative data only

  • That is because skew and symmetry do not make sense for categorical data, e.g. "favorite colour"

Stemplots

What is a stem-and-leaf plot?

• A stem-and-leaf plot (stemplot) is a simple way to display an ordered list of quantitative (numerical) data using digits

• Two-digit numbers are split into a tens digit (the stem) and a units digit (the leaf)

  • 25 becomes 2 | 5

  • The stem is written vertically and the leaves are written horizontally (in order)

• The following diagram shows the ages below

  • 11, 18, 20, 21, 25, 28, 29, 35, 36, 40

Key: 1|8 means 18 years old

What is the key on a stem-and-leaf plot?

• The key shows how values are formed from digits

  • It should include units

• Other keys are possible

  • 2 | 5 represents 2.5 degrees

  • 2 | 5 represents 2005 people

How do I find the median from a stem-and-leaf plot?

• The median is the middle number

  • Data values are already in order

  • You can cross out numbers from the beginning and end until they meet in the middle

    • Remember that the highest number will be at the end of the last stem

    • If two numbers remain in the middle, find the midpoint between them

Can I use stem-and-leaf plots to comment on the shape of the distribution?

• You can use stem-and-leaf plots to comment on the shape of the distribution of the data

  • such as the skew or symmetry of the data

• The easiest way to visualize the shape of the distribution is by imagining a rotation of the stem and leaf plot 90 counterclockwise