Question

Arsenic in Rice Listed below are measured amounts (mg per serving) of arsenic in a sample of servings of brown rice [data from the Food and Drug Administration (FDA)]. Construct a frequency distribution. Use a class width of 2 mg, and use 0 mg as the lower class limit of the first class.

6.1 5.4 6.9 4.9 6.6 6.3 6.7 8.2 7.8 1.5 5.4 7.3

Short answer

The following frequency distribution table is constructed for the amounts of arsenic present in the servings of brown rice:

Amount of Arsenic (microgram per serving)	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

Step-by-step solution

Given information

The sample comprises the amounts of arsenic (mg per serving) present in a set of 12 brown rice servings.

Frequency distribution

In a set of values for a given variable, such that any value is repeatable, a grouped frequency distribution can be constructed to summarize the counts of values.

It is created using categories or class intervals for the values of the variable.

The corresponding frequencies of each class interval can be tabulated to obtain the frequency distribution table.

Construction of the frequency distribution table

The class width for each class interval is 2 mg.

The first class interval has 0 mg as the lower limit.

Here, 0.0 is the lower limit of the first class, and the maximum value is 7.8 for the data set. The class intervals are defined as shown below.

Amount of Arsenic (mg per serving)

0.0–1.9

2.0–3.9

4.0–5.9

6.0–7.9

8.0–9.9

Here, both the upper and the lower limits are included in the class interval, resulting in a class width of 2 mg. This results in discontinuous class intervals. Such a frequency distribution is called aninclusive frequency distribution.

The number of values that occur in each interval give the following frequency distribution table.

Amount of Arsenic (microgram per serving)	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

Thus, the table provides the required frequency distribution.