Question

Eat your beans! Beans and other legumes are a great source of protein. The following data give the protein content of 30 different varieties of beans, in grams per 100 grams of cooked beans

Part (a). Make a stemplot of these data.

Part (b). What interesting feature does the graph reveal?

Part (c). What proportion of these bean varieties contain more than 9 grams of protein per 100 grams of cooked beans?

Short answer

Part (a)

Stem	Leaf
6	8
7	0 1 5 5 6 7 8 8
8	0 1 1 2 2 3 3 3 7 9 9
9	0 0 0 1 2 3 5 7
10	6
11
12
13	5

$\overline{)key:31}1means3.1$

Part (b) 13.5 grams per 100 cooked beans is a possible outlier.

Part (c) 0.2333

Step-by-step solution

Part (a) Step 1. Given information. 

7.5, 8.2, 89, 9.3, 7.1, 8.3, 8.7. 9.5, 8.2, 9.1, 90, 90, 97, 92 89, 8.1, 90, 7.8, 8.0, 7.8, 7.0, 7.5, 13.5, 8.3, 6.8, 10.6, 8.3, 76, 77, 8.1

Part (a) Step 2. Create a stemplot from these data.

Let us now order the data values from smallest to largest.

6.8, 7.0, 7.1. 7.5, 7.5, 7.6, 77, 78, 7.8, 8.0, 8.1, 8.1, 82, 82, 83, 8.3, 8.3.

8.7, 8.9, 8.9, 90, 9.0, 9.0, 9.1, 92, 93, 9.5, 9.7, 10.6, 13.5

Make a vertical line.

Place the ones to the left of the vertical line and the tenths of each data value to the right of the vertical line

Stem	Leaf
6	8
7	0 1 5 5 6 7 8 8
8	0 1 1 2 2 3 3 3 7 9 9
9	0 0 0 1 2 3 5 7
10	6
11
12
13	5

$\overline{)key:31}1means3.1$

Part (b) Step 1. Interesting feature does the graph reveal 

We notice a gap between 13.5 and the remaining data values in the stemplot, indicating that 13.5 grams per 100 grams of cooked beans is a possible outlier.

As a results:

13.5 grams per 100 cooked beans is a possible outlier.

Part (c) Step 1. Proportion of these bean varieties contain more than 9 grams of protein per 100 grams of cooked beans. 

Then we notice that 7 of the 30 data values are greater than 9 (specifically, 9.1, 9.2, 9.3, 9.5, 9.7, 10.6, and 13.5).

$\frac{7}{30}\approx 0.2333$

This means that approximately 0.2333 of these bean varieties have more than 9 grams of protein per 100 grams of cooked beans.