Students make a histogram of their typical-student data and then write a summary of what the histogram shows.
Students are introduced to histograms, using the line plot to build them. They investigate how the bin width affects the shape of a histogram. Students understand that a histogram shows the shape of the data, but that measures of center or spread cannot be found from the graph.
- A histogram groups data values into intervals and shows the frequency (the number of data values) for each interval as the height of a bar.
- Histograms are similar to line plots in that they show the shape and distribution of a data set. However, unlike a line plot, which shows frequencies of individual data values, histograms show frequencies of intervals of values.
- We cannot read individual data values from a histogram, and we can't identify any measures of center or spread.
- Histograms sometimes have an interval with the most data values, referred to as the mode interval.
- Histograms are most useful for large data sets, where plotting each individual data point is impractical.
- The shape of a histogram depends on the chosen width of the interval, called the bin width. Bin widths that are too large or too small can hide important features of the data.
Goals and Learning Objectives
- Learn about histograms as another tool to describe data.
- Show that histograms are used to show the shape of the data for a wider range of data.
- Compare a line plot and histogram for the same set of data.