To construct the stem-and-leaf plot for the given data where the leaf represents the hundredths digit, follow these steps:
1. Identify the Stems and Leaves:
- The stems represent the integer part of the numbers.
- The leaves represent the hundredths part of the numbers.
2. Sort and Arrange the Stems and Leaves:
- Group the data based on the integer part (stem).
- Sort the leaves (hundredths part) in ascending order for each stem.
Given Data:
[tex]\[ 4.91, 5.08, 4.99, 5.04, 4.82, 5.26, 5.06, 4.96, 5.24, 5.07, 5.11, 4.88, 5.03, 4.91, 5.23, 4.87, 5.08, 5.16, 5.02, 4.98, 4.81, 5.21, 5.09, 4.85, 5.13, 5.09 \][/tex]
Let's group them by their stems:
- For stem [tex]\(4\)[/tex]:
[tex]\[
[4.91, 4.99, 4.82, 4.96, 4.88, 4.91, 4.87, 4.98, 4.81, 4.85]
\][/tex]
Corresponding leaves:
[tex]\[
91, 99, 82, 96, 88, 91, 87, 98, 81, 85
\][/tex]
- For stem [tex]\(5\)[/tex]:
[tex]\[
[5.08, 5.04, 5.26, 5.06, 5.24, 5.07, 5.11, 5.03, 5.23, 5.08, 5.16, 5.02, 5.21, 5.09, 5.13, 5.09]
\][/tex]
Corresponding leaves:
[tex]\[
08, 04, 26, 06, 24, 07, 11, 03, 23, 08, 16, 02, 21, 09, 13, 09
\][/tex]
3. Sort the Leaves:
- For stem [tex]\(4\)[/tex], the sorted leaves are:
[tex]\[
81, 82, 85, 87, 88, 91, 91, 96, 98, 99
\][/tex]
- For stem [tex]\(5\)[/tex], the sorted leaves are:
[tex]\[
02, 03, 04, 06, 07, 08, 08, 08, 09, 09, 11, 13, 16, 21, 23, 24, 26
\][/tex]
4. Construct the Plot: Present the data in a stem-and-leaf format.
Thus, the stem-and-leaf plot for the given data is:
[tex]\[
\begin{tabular}{l|l}
4 & 81828587889191969899 \\
5 & 0203040607080808090911 13621232426
\end{tabular}
\][/tex]
