Three Popular Data Displays

ANSWERS

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

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

Frequency and relative frequency histograms are similarly generated.

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.

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

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

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{matrix} Length & 80 \sim 89 & 90 \sim 99 & 100 \sim 109 \\ f & 1 & 1 & 5 \end{matrix}

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

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

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

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. $20$ .