## Three Popular Data Displays

This section elaborates on how to describe data. In particular, you will learn about the relative frequency histogram. Complete the exercises and check your answers.

1. The vertical scale on one is the frequencies and on the other is the relative frequencies.

1. $\begin{array}{r|lllllll} 5 & 3 & & & & & \\ 6 & 8 & 9 & & & & \\ 7 & 0 & 0 & 0 & 5 & 6 & 7 & \\ 8 & 0 & 2 & 3 & 5 & 5 & 5 & 8 \\ 9 & 2 & 3 & 6 & & & \\ 10 & 0 & & & & & \end{array}$

Frequency and relative frequency histograms are similarly generated.

1. Noting that $n=10$ the relative frequency table is:

$\begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline f / n & 0.3 & 0.4 & 0.2 & 0.1 \end{array}$

Since $n$ is unknown, $a$ is unknown, so the histogram cannot be constructed.

$\begin{array}{r|l|llll} 8 & 7 & & & \\ 9 & 9 & & & \\ 10 & 0 & 5 & 5 & 7 & 8 \\ 11 & 8 & 9 & & & \\ 12 & 5 & & & \end{array}$

Frequency and relative frequency histograms are similarly generated.

1. $\text { Noting } n=300 \text {, the relative frequency table is therefore: }$

$\begin{array}{c|cccc} \text { Blood Type } & O & A & B & A B \\ \hline f / n & 0.4533 & 0.4 & 0.1067 & 0.04 \end{array}$

A relative frequency histogram is then generated.

The stem and leaf diagrams listed for Samples 1, 2, and 3 in that order.

 $6$ $7$ $8$ $7$ $9$ $9$ $10$ $0 \quad 5 \quad 5 \quad 7 \quad 8$ $11$ $8 \quad 9$ $12$ $5$ $13$ $14$ $15$ $16$ $6$ $7$ $8$ $9$ $10$ $11$ $12$ $13$ $3\quad 7 \quad 8 \quad 8 \quad 9$ $14$ $0 \quad 2 \quad 5$ $15$ $2$ $16$ $0$ $6$ $0$ $9$ $7$ $4$ $4 \quad 9$ $8$ $0$ $0 \quad 2 \quad 2 \quad 2 \quad 2 \quad 3 \quad 3$ $9$ $10$ $11$ $12$ $13$ $14$ $15$ $16$
The frequency tables are given below in the same order.

$\begin{array}{c|ccc} \text { Length } & 130 \sim 139 & 140 \sim 149 & 150 \sim 159 \\ \hline f & 5 & 3 & 1 \end{array}$

$\begin{array}{c|c} \text { Length } & 160 \sim 169 \\ \hline f & 1 \end{array}$

$\begin{array}{c|ccc} \text { Length } & 60 \sim 69 & 70 \sim 79 & 80 \sim 89 \\ \hline f & 1 & 2 & 7 \end{array}$

The relative frequency tables are given below in the same order.

$\begin{array}{c|ccc} \text { Length } & 80 \sim 89 & 90 \sim 99 & 100 \sim 109 \\ \hline f / n & 0.1 & 0.1 & 0.5 \end{array}$

$\begin{array}{c|cc} \text { Length } & 110 \sim 119 & 120 \sim 129 \\ \hline f / n & 0.2 & 0.1 \end{array}$

$\begin{array}{c|ccc} \text { Length } & 130 \sim 139 & 140 \sim 149 & 150 \sim 159 \\ \hline f / n & 0.5 & 0.3 & 0.1 \end{array}$

$\begin{array}{c|c} \text { Length } & 160 \sim 169 \\ \hline f / n & 0.1 \end{array}$

$\begin{array}{c|ccc} \text { Length } & 60 \sim 69 & 70 \sim 79 & 80 \sim 89 \\ \hline f / n & 0.1 & 0.2 & 0.7 \end{array}$

1. $19$.
2. $20$.