First, organize the data in five intervals. The first interval is between 70 and 74.
Diagram:
Standard deviation: 6.8 Mean: 79.5
Practice makes perfect
Let's begin by organizing the given data so that we can draw the histogram. Notice that each bin should have a width of 4mph so that it is evenly spaced.
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70 ≤ x < 74 & 70, 70, 71, 72, 73, 73
74 ≤ x < 78 & 74, 75, 75
78 ≤ x < 82 & 80, 80
82 ≤ x < 86 & 83, 84, 85, 85
86 ≤ x < 90 & 86, 88, 88, 89, 89
Now we can draw the histogram.
As we can see, most observations are away from the center which means drivers are generally driving too fast or too slow.
Adding the boxplot
To draw the boxplot, we must find the minimum value, Q1, the median, Q3, and the maximum value. We can do that with a graphing calculator. First, enter the values into lists by pushing STAT. Next, choose Edit, and enter the values in the first column.
To calculate the different measurements that we need, push STAT and scroll right until you reach CALC. Choose the first option, 1-Var Stats.
As we can see, the center, which is the same as the median, is at 80. Finally, we can add the boxplot to our histogram.
Since there are no outliers, both the mean and the standard deviation are appropriate measures for describing the spread.
