In this lesson students are introduced to histograms. They learn that, like a dot plot, a histogram can be used to show the distribution of a numerical data set, but unlike a dot plot, a histogram shows the frequencies of groups of values, rather than individual values. Students analyze the structures of dot plots and histograms displaying the same data sets and determine what information is easier to to understand from each type of display (MP7). Students read and interpret histograms in context (MP2) to prepare them to create a histogram.
- Compare and contrast (orally) dot plots and histograms in terms of how useful they are for answering different statistical questions.
- Create a histogram to represent a data set.
- Interpret a histogram to answer (in writing) statistical questions about a data set.
Let's explore how histograms represent data sets.
- I can recognize when a histogram is an appropriate graphical display of a data set.
- I can use a histogram to get information about the distribution of data and explain what it means in a real-world situation.
The center of a set of numerical data is a value in the middle of the distribution. It represents a typical value for the data set.
For example, the center of this distribution of cat weights is between 4.5 and 5 kilograms.
The distribution tells how many times each value occurs in a data set. For example, in the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.
Here is a dot plot that shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35.
The frequency of a data value is how many times it occurs in the data set.
For example, there were 20 dogs in a park. The table shows the frequency of each color.
color frequency white 4 brown 7 black 3 multi-color 6
A histogram is a way to represent data on a number line. Data values are grouped by ranges. The height of the bar shows how many data values are in that group.
This histogram shows there were 10 people who earned 2 or 3 tickets. We can't tell how many of them earned 2 tickets or how many earned 3. Each bar includes the left-end value but not the right-end value. (There were 5 people who earned 0 or 1 tickets and 13 people who earned 6 or 7 tickets.)
The spread of a set of numerical data tells how far apart the values are.
For example, the dot plots show that the travel times for students in South Africa are more spread out than for New Zealand.