Chapter 14.3, Problem 4MCQ

To determine

To show: The stem-and-leaf plot of the test scores.

Answer to Problem 4MCQ

  $\begin{array}{cc}\text{stem}& \text{leaf}\\ 5& \begin{array}{cc}4& 5\end{array}\\ 6& \begin{array}{ccc}2& 4& 5\end{array}\\ 7& \begin{array}{cccc}1& 5& 6& \begin{array}{ccc}7& 8& 9\end{array}\end{array}\\ 8& \begin{array}{cccc}0& 2& 4& \begin{array}{cccc}5& 6& 7& \begin{array}{cc}8& 9\end{array}\end{array}\end{array}\\ 9& \begin{array}{cccc}0& 2& 3& \begin{array}{ccc}5& 6& \begin{array}{cc}8& 9\end{array}\end{array}\end{array}\end{array}$

Explanation of Solution

Given information:

  

Formula used:

Stem-and-Leaf Plot − Each item of the data is separated into two parts that are used to form a stem and a leaf.

Stem :- The column on the left shows the stems. It consist of the digits in the greatest common place value of all the data.

Leaves :- The column at the right contains the leaves . The leaves are one-digit numbers, which are in the next greatest place value after the stem.

The stems and leaves are arranged from least to greatest.

Calculation:

Consider the data in ascending order,

  $\left\{\begin{array}{l}54,55,62,62,64,65,71,75,76,77,78,\\ 79,80,82,84,85,86,87,88,89,89,89,\\ 90,92,93,93,95,96,98,99\end{array}\right\}$

Now, making the table

Scores	Frequency
54	1
55	1
62	2
64	1
65	1
71	1
75	1
76	1
77	1
78	1
79	1
80	1
82	1
84	1
85	1
86	1
87	1
88	1
89	3
90	1
92	1
93	2
95	1
96	1
98	1
99	1

Using the above table in stem-and-leave plot we get ,

  $\begin{array}{cc}\text{stem}& \text{leaf}\\ 5& \begin{array}{cc}4& 5\end{array}\\ 6& \begin{array}{ccc}2& 4& 5\end{array}\\ 7& \begin{array}{cccc}1& 5& 6& \begin{array}{ccc}7& 8& 9\end{array}\end{array}\\ 8& \begin{array}{cccc}0& 2& 4& \begin{array}{cccc}5& 6& 7& \begin{array}{cc}8& 9\end{array}\end{array}\end{array}\\ 9& \begin{array}{cccc}0& 2& 3& \begin{array}{ccc}5& 6& \begin{array}{cc}8& 9\end{array}\end{array}\end{array}\end{array}$

Since the range is from 54-99. This implies the common place value of all the data is tens place. The right column shows the leaves of the data . Both stems and leaves are arranged in ascending order.