Bar Charts & Histograms (College Board AP® Statistics)

Bar charts

What is a bar chart?

• A bar chart is used to visualize the data when working with one categorical variable

• The categories of the variable are labeled on one axis

• The frequency or relative frequency is labeled on the other axis

• The height of each bar represents the frequency or relative frequency of that category

• There are gaps between the bars

What information can be found from a bar chart?

• You can find the mode of the variable

  • It is the category with the tallest bar

• You can rank the categories by their frequencies

Histograms

What is a histogram?

• A histogram is used to visualize the data when working with one quantitative variable

  • The variable can be discrete or continuous

• The values of the variable are labeled on the horizontal axis

• The frequency or relative frequency is labeled on the vertical axis

• The data might be grouped into non-overlapping intervals of equal width

  • The intervals can be referred to as bins

  • The width of the intervals affects the shape of the histogram

• The height of each bar represents the frequency or relative frequency of data points that lie in that interval

• There are no gaps between the bars

What information can be found from a histogram?

• You can find the modal group of the variable

  • It is the interval with the tallest bar

• If the data is ungrouped then you can find

  • the mean

  • the median

  • the range

• You can see the shape and skewness of the distribution

What information cannot be found from a histogram?

• If the data is grouped then you cannot find the exact values for:

  • the median

    • You can only find the interval which contains the median

      • e.g. if the histogram represents 25 people, find the interval containing the 13^th person

  • the mean

    • You can estimate the mean by using the midpoint for each interval

  • the range

    • You can find the smallest and largest possible values for the range

      • e.g. if the first interval is and the last is then the smallest the range can be is and the largest the range can be is