Dot Plots and Histograms

Lesson 8.03

After completing this lesson, you will be able to say:

• I can create a dot plot and histogram to display a set of numerical data.

• I can identify the components of dot plots and histograms.

• I can identify the shape of data using a graphical representation.

Dot Plots

Dot plot:

A graphical display of data using dots to show the frequency of each data value.

To create a dot plot:

• Draw a horizontal line using an appropriate range (or category).

• Place a dot over the data value for each frequency in the data set.

• Label the horizontal line and title the graph.

Creating a Dot Plot

Take Wesley’s class data and list it in order to identify the least and greatest values:

8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 13

This list shows that you should draw a number line ranging from eight to thirteen.

Next, place a dot above the number line for each time that number occurs in the data set. Eight occurs once, so place one dot above eight. Nine occurs twice, so place two dots above nine.Ten occurs four times, so place four dots above ten, and so on.

Because there are eleven values in the data set, there will be eleven dots on the graph.

Last, label the horizontal line and give it a title. The data points represent the frequency of dandelions.

Creating a Dot Plot

Next, place a dot above the number line for each time that number occurs in the data set. Eight occurs once, so place one dot above eight.

Nine occurs twice, so place two dots above nine.

Continue until you have placed a dot for each value in your data set

Example of a Numerical Dot Plot

Notice, we placed a dot about the number on the number line, more than 1 dot over a number would represent how many times the number appeared

Example of a Categorical Dot Plot

Try it

Check your work

Histograms

Histogram:

A graph that uses vertical columns, or bars, to show the frequency of data, or intervals of data.

To create a histogram: • Group the data values into appropriate bin intervals and determine the

frequency.• Draw and label the horizontal and vertical axes.• Draw bars to a certain height based on the frequency of each bin.• Do not put spaces between the bars.• Remember to title the graph.

Creating a Histogram

To determine the interval for each bin, first organize the data set from least to greatest. Then, group the data together to ensure the interval for each bin is the same.

You choose the size of each bin so that it shows your data in the best light. Because the numbers in the data set go from one to thirty-five, the best intervals for this set of data would be groups of fives. Interval 1: 1- 5, Interval 2: 6 – 10 and so on

Creating a Histogram

Draw and label the horizontal axis.

draw a horizontal axis. Divide the line into seven sections, because seven bins were created for this data set. Label each bin to show the interval of the values in that bin. This marks where to draw each bar. Remember, there are no spaces between the bars in histograms, so do not space the bins.

Creating a Histogram

Draw and label the vertical axis.

Next, draw and label the vertical axis. This line shows the frequency of the values in each bin. Because the smallest bin has a frequency of one and the biggest bin has a frequency of five, choose appropriate increments that allow you to see all the bin heights. For this set, let's have the vertical line go up to six.

Creating a Histogram

Now you can draw each bar. Bin one contains three data values, so the first bar goes up to a height of three. Continue drawing the bars for each Bin. Remember, Bins five and six do not have values, so there do not include a bar in those spaces

Draw the bars.

Creating a Histogram

Color and Title.

To finalize the histogram, you can color the bars so that it is easier to read. However, this is up to you; you don't have to add color to the bars. Go ahead and finalize your histogram by giving it a title.

Try it!

A worker collected data to see the prices, in whole dollars, of video games on display for the week. The results are shown below:

10, 10, 21, 25, 25, 28, 30, 35, 40, 43, 44, 45, 48, 58, 59

Create a histogram to represent the data.

Check your work

Trends

A trend is the general drift or tendency in a set of data.

Trend can help determine if the data are symmetric or asymmetric. They can even identify clusters, peaks, and gaps within the distribution of the data.

Peak:The value in the data set that occurs the most often.

Cluster:A group of data points gathered around a specific value.

Gap:A large space between data points.

Symmetry:A distribution that can be divided at the center so each half is a mirror image of the other

Asymmetric A distribution that has values occurring at various frequencies.

Examples with trends

This dot plot is symmetric with a peak at 10. Because the data are symmetric and the peak is toward the center, they create a bell-shaped curve. This is known as “normal distribution of a data set.”

Examples with trends

This data set is asymmetric and has a peak at 9. It also contains two clusters on each end, where the majority of the data values is grouped. This forms a gap between the two clusters where no data points are located.

Examples with trends

In this graph, the data set is spread equally across the range of distribution. There are no unique peaks, gaps, or clusters. This type of distribution is called a “uniform distribution.“

Uniform:

When each value in the distribution occurs the same amount.

Try it

What conclusions can you make about the shape of the following dot plot?

Check your work

The graph is asymmetric, with no gaps. It peaks at 4

Now that you completed this lesson, you should be able to say:

• I can create a dot plot and histogram to display a set of numerical data.

• I can identify the components of dot plots and histograms.

• I can identify the shape of data using a graphical representation.