Q.2.99 - Elementary Statistics

Question

University Patents. The number of patents a university receives is an indicator of the research level of the university. From a study titled Science and Engineering Indicators issued by the National Science Foundation, we found the number of U.S. patents awarded to a sample of $36$ private and public universities to be as follows.

Construct a stem-and-leaf diagram for these data with

a. one line per stem.

b. two lines per stem.

c. Which stem-and-leaf diagram do you find more useful? Why?

Step-by-Step Solution

Answer

a). One line per stem:

b). Two lines per stem:

c). The one line per stem plot is more useful. 

Part (a) Step 1: Given Information

The data is given as,

Part (a) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Create a vertical line to plot a stem-and-leaf diagram.

Place the tens digits to the left of the vertical line and the ones digits to the right of the vertical line for each data value.

Part (b) Step 1: Given Information

The data is given as,

Part (b) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Create a vertical line to plot a stem-and-leaf diagram.

Place the tens digits to the left of the vertical line and the ones digits to the right of the vertical line for each data value.

Part (c) Step 1: Given Information

The data is given as,

Part (c) Step 2: Explanation

Concept:

Place the digits of the tens to the left of the vertical line in the stem-and-leaf diagram, and the digits of the ones to the right of the vertical line.

Calculation:

Because there are so many stems and the other plot is too big, the one line per stem layout is more practical.