## Presenting Data

#### LEARNING OBJECTIVE

1. To learn two ways that data will be presented in the text.

In this book we will use two formats for presenting data sets. The first is a data list, which is an explicit listing of all the individual measurements, either as a display with space between the individual measurements, or in set notation with individual measurements separated by commas.

#### EXAMPLE 1

The data obtained by measuring the age of 21 randomly selected students enrolled in freshman courses at a university could be presented as the data list

$\begin{array}{lllllllllll}18 & 18 & 19 & 19 & 19 & 18 & 22 & 20 & 18 & 18 & 17 \\ 19 & 18 & 24 & 18 & 20 & 18 & 21 & 20 & 17 & 19 & \end{array}$

or in set notation as

$\{18,18,19,19,19,18,22,20,18,18,17,19,18,24,18,20,18,21,20,17,19\}$

A data set can also be presented by means of a data frequency table, a table in which each distinct value $x$ is listed in the first row and its frequency $f$, which is the number of times the value $x$ appears in the data set, is listed below it in the second row.

#### EXAMPLE 2

The data set of the previous example is represented by the data frequency table

$\begin{array}{c|ccccccc} x & 17 & 18 & 19 & 20 & 21 & 22 & 24 \\ \hline f & 2 & 8 & 5 & 3 & 1 & 1 & 1 \end{array}$

The data frequency table is especially convenient when data sets are large and the number of distinct values is not too large.

#### KEY TAKEAWAY

• Data sets can be presented either by listing all the elements or by giving a table of values and frequencies.

#### EXERCISES

List all the measurements for the data set represented by the following data frequency table.

$\begin{array}{c|ccccc} x & 31 & 32 & 33 & 34 & 35 \\ \hline f & 1 & 5 & 6 & 4 & 2 \end{array}$

List all the measurements for the data set represented by the following data frequency table.

$\begin{array}{c|cccccccc} x & 97 & 98 & 99 & 100 & 101 & 102 & 103 & 105 \\ \hline f & 7 & 5 & 3 & 4 & 2 & 2 & 1 & 1 \end{array}$

Construct the data frequency table for the following data set.

$\begin{array}{llllll}22 & 25 & 22 & 27 & 24 & 23 \\ 26 & 24 & 22 & 24 & 26\end{array}$

Construct the data frequency table for the following data set.

$\begin{array}{r} \{1,5,2,3,5,1,4,4,4,3,2,5,1,3,2 \\ 1,1,1,2\} \end{array}$

1. $\{31,32,32,32,32,32,33,33,33,33,33,33,34,34,34,34,35,35\}$
2. $\begin{array}{c|cccccc} x & 22 & 23 & 24 & 25 & 26 & 27 \\ \hline f & 3 & 1 & 3 & 1 & 2 & 1 \end{array}$. This text was adapted by Saylor Academy under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License without attribution as requested by the work's original creator or licensor.