## 1.3 Presentation of 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 listAn explicit listing of all the individual measurements made on a sample., 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

$181819191918222018181719182418201821201719$

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 tableA table listing each distinct value x and its frequency f., a table in which each distinct value x is listed in the first row and its frequencyHow often a value x appears in a data set. 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

$x17181920212224f2853111$

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

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

$x3132333435f15642$
2. List all the measurements for the data set represented by the following data frequency table.

$x979899100101102103105f75342211$
3. Construct the data frequency table for the following data set.

$2225222724232624222426$
4. Construct the data frequency table for the following data set.

${1,5,2,3,5,1,4,4,4,3,2,5,1,3,2,1,1,1,2}$

2. $x222324252627f313121.$