Q.22 - Elementary Statistics

Question

 Battery Lifetime. In the article "Comparing the lifetime of two brands of batteries" (Joumal of Statistics Education, Vol. 21, No, 1. pp. 1-19) by P. Dunn, two brands of AA alkaline batteries were compared. The following table gives the number of pulses required for a sample of 18 Energizer and Ultracell batteries to reach a voltage level of $1.3$

a. Construct a stem-and-leaf diagram for these data with one line per stem.

b. Construct a stem-and-leaf diagram with two lines per stem.

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

Step-by-Step Solution

Answer

(a)

(b)

(C) Second diagram is most useful

Part (a) Step 1 :Given Information

The given data is :

we have to Construct a stem-and-leaf diagram for these data with one line per stem 

Part (a) Step 2: Explanation

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

Part (b) Step 1 :Given Information

The given data is:

we have to Construct a stem-and-leaf diagram with two lines per stem. 

Part (b) Step 2: Explanation

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

Part (c) Step 1 :Given Information

The given data is 

we have to find out which diagram is more useful

Part (c) Step 2: Explanation

The number of data values that fall into a class is known as frequency.

The second diagram is more useful because the first diagram only has four stems, making it difficult to see the data distribution.

As a result, the second diagram is more useful.