Question

Histogram Use the frequency distribution from Exercise 1 to construct a histogram. Use class midpoint values for the horizontal scale.

Short answer

The given histogram is plotted for the frequency distribution table of the measured amounts of arsenic in a sample of servings of brown rice:

Step-by-step solution

Given information

A frequency table is constructed for the measured amounts of arsenic ( g per serving) in a sample of servings of brown rice.

Histogram

A graph that shows frequencies (on the vertical axis) of different class intervals (on the horizontal axis) is called a histogram. In a histogram, the vertical bars have the same width and are adjacent to each other. The height of the bars represents the frequencies of the classes.

Plotting the histogram

The given frequency distribution is utilised to construct the histogram:

Amount of Arsenic	Frequency
0.0-1.9	1
2.0-3.9	0
4.0-5.9	3
6.0-7.9	7
8.0-9.9	1

The midpoint formula for computing the midpoints is as follows:

$\text{Midpoint}=\frac{\text{lower}\text{class}\text{limit}+\text{upper}\text{class}\text{limit}}{2}$

Since they are required to plot the midpoints on the horizontal scale, the midpoints of the class intervals are computed as shown below:

$$\begin{gathered} {\text{Midpoint}}_1=\frac{0.0+1.9}{2} \\ =0.95 \\ {\text{Midpoint}}_2=\frac{2.0+3.9}{2} \\ =2.95 \end{gathered}$$

$$\begin{gathered} {\text{Midpoint}}_3=\frac{4.0+5.9}{2} \\ =4.95 \\ {\text{Midpoint}}_4=\frac{6.0+7.9}{2} \\ =6.95 \end{gathered}$$

$$\begin{gathered} {\text{Midpoint}}_5=\frac{8.0+9.9}{2} \\ =8.95 \end{gathered}$$

The following histogram is constructed by considering the midpoints on the horizontal axis and making vertical bars according to the frequency of each interval without any gaps.