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.

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.

	$6$
	$7$
	$8$	$7$
	$9$	$9$
	$10$	$0 \quad 5 \quad 5 \quad 7 \quad 8$
	$11$	$8 \quad 9$
	$12$	$5$
	$13$
	$14$
	$15$
	$16$
	$6$
	$7$
	$8$
	$9$
	$10$
	$11$
	$12$
	$13$	$3\quad 7 \quad 8 \quad 8 \quad 9$
	$14$	$0 \quad 2 \quad 5$
	$15$	$2$
	$16$	$0$
$6$	$0$	$9$
$7$	$4$	$4 \quad 9$
$8$	$0$	$0 \quad 2 \quad 2 \quad 2 \quad 2 \quad 3 \quad 3$
$9$
$10$
$11$
$12$
$13$
$14$
$15$
$16$