# 1.3: Presentation of Data

Learning Objectives

• 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 $$\PageIndex{1}$$

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:

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

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.

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 $$\PageIndex{2}$$

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

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

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.

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