Question

For instance, consider the grouped days-to-maturity data given in Table $2.10$(b) on page $57$.

From that table, we see that the cumulative frequency of investments with a maturity period of less than $50$day is $4(3+1)$and, therefore, the cumulative relative frequency is$0.1(4/40)$.

Table $2.14$shows all cumulative information for the days-to-maturity data.

Cumulative information for days-to-maturity data.

a. Round each observation to the nearest year and then construct a stem-and-leaf diagram of the rounded data.

b. Truncate each observation by dropping the decimal part, and then construct a stem-and-leaf diagram of the truncated data.

c. Compare the stem-and-leaf diagrams that you obtained in parts (a) and (b).

Short answer

(a) The stem and leaf diagram is shown in figure

(b) The stem and leaf diagram for truncated data is shown in figure.

(c) The diagrams have nearly identical pattern.

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that, the table which shows the cumulative information for the days-to-maturity data.

We have to round each observation to the nearest year and then construct a stem-and-leaf diagram of the rounded data.

Part (a) Step 2: Explanation 

Create a stem-and-leaf diagram using the closest year.

The data is rounded to

$76,84,87,75,83,78,76,53,56,54,88,79,82,54,53,59,98,66,86,72$

Below is a stem and leaf diagram for rounded data.

Part (b) Step 1: Given Information 

Given in the question is a table, which shows the cumulative information for the days to maturity data. We have to truncate each observation by dropping the decimal part, and then construct a stem-and-leaf diagram of the truncated data.

Part (b) Step 2: Explanation 

Each observation's abbreviated data is displayed below.

$75,83,87,74,72,78,76,52,56,53,88,78,81,54,52,58,97,65,86,72$

For truncated data, the stem and leaf diagram is displayed below.

For truncated data, the stem and leaf diagram is displayed below.

Part (c) Step 1: Given Information 

Given in the question is a table, we have to compare the stem-and-leaf diagrams that you obtained in parts (a) and (b).

Part (c) Step 2: Explanation 

Center, spread, form, and distinctive features are all phrases used to describe data patterns. Asymmetric, bell-shaped, skewed, and other descriptive terms are used to describe some frequent distributions.

It's worth noting that the stem and leaf diagram patterns are essentially identical in both graphs.