Once you have constructed a dotplot, you can begin to see where the data are centered and how the data are spread out. Do you see any interesting features in this set of data?

Here are the data the researchers collected. To get a better picture of the data, you can create graphs that display the data in different ways. Start by constructing a dotplot. Plot each observation on a number line.

You can also create a histogram by collapsing the data into classes. For this histogram, you could use a class width of 1 second.

Now that the histogram is complete, do you have a better idea of how long it typically takes a person to react to hazards on the roadway while writing a text message?

Another graphical display you can create is a boxplot. To construct a boxplot, there are five numbers you need to calculate: the minimum, the lower quartile, the median, the upper quartile, and the maximum. To find the values for the five-number summary, it is helpful to order the data from smallest to largest.

With the data ordered in this way, it will be easier to find the five-number summary.

Do you remember how to find the five-number summary for a set of data?

Start by entering the minimum and maximum values and the median of the data set in the blanks. Remember, the median value is the number in the middle once the data have been ordered from least to greatest. Check your answers when you are finished.

Good job. Now enter the value for quartiles 1 and 3. Remember, to find the value for Q1, find the median of the lower half of the data set. To find the value for Q3, find the median of the upper half of the data set.

Try again. The minimum and maximum are the smallest and largest values of the data set. Remember, the median value is the number in the middle once the data have been ordered from least to greatest. Since there are 20 data points, the number in the middle is the average of the 10th and 11th values.

Not quite. The smallest value is 2.1 and the largest value is 8. The 10th value is 4.4 and the 11th value is 4.5. The number in the middle of 4.4 and 4.5 is 4.45. This is the median. Now enter the value for quartiles 1 and 3. Remember, to find the value for Q1, find the median of the lower half of the data set. To find the value for Q3, find the median of the upper half of the data set.

Excellent work! You remember how to find the five-number summary for a data set. Move to the next panel to create a boxplot for the data set.

Try again. The lower half of the data values range from 2.1 to 4.4. What is the median of the first ten data points? The upper half of the data values range from 4.5 to 8. What is the median of the last ten data points?

Not quite. The median of the first ten data points is the average of the 5th and 6th values. This number is 3.2. The median of the last ten data points is the average of the 15th and 16th values. This number is 5.55. Move to the next panel to create a boxplot for the data set.

Now use the five-number summary to create a boxplot for the data. Drag the sliders to the appropriate places on the number line. Check your work when you are finished.

Good job! You remember how to construct a boxplot.

Try again. At least one of the numbers is not graphed correctly.

The correct boxplot is shown.

Another numerical display is a stem-and-leaf plot.

The leaves are presented from least to greatest.

Every stem-and-leaf plot needs a key that indicates the units of the data and shows how the data should be interpreted.