Collecting and analyzing data

Organizing data

The following data represents the number of points scored by an NBA player during games played in January, 2006:

Consider the way this data is displayed. Is this list format helpful? Why or why not?

Examine this data again. How might you display this data to make it more meaningful? Describe how you would organize the data. What other methods could be used?

How can we organize data?

Data can be organized in a variety of ways. Some examples are a frequency table, stem-and-leaf plot, and a relative frequency table.

Frequency tables

Frequency tables are tables where data is organized into categories. Categories are listed along with the number of times they occur. In other words, categories are listed with their corresponding frequencies.

In this frequency table, there are three flower types: Daisy, Rose, Violet.

Daisy has a group of 5 tally marks, and a frequency of 5.

Rose has a group of 5 tally marks and 3 individual tally marks, and a frequency of 8.

Violet has two groups of 5 tally marks and 1 individual tally mark, and a frequency of 11.

Stem-and-leaf plot

A stem-and-leaf plot is an organization of a set of quantitative data where each data value is split into two parts, a “stem” and a “leaf.”

In a stem-and-leaf plot, stems are listed in the first column and leaves are listed in the second column.

The stem-and-leaf plot represents these test results: 17, 22, 46, 34, 52, 19, 21, 13, 15, 20, 21, 30, 40, 45.

The stem shows the first digit of the number, tens, and is written in the left column.

The leaf is the last digit of the number, the ones digit, and is listed in the right column. The leaves are listed from least to greatest.

Relative frequency table

A relative frequency table is where data is organized into categories with corresponding frequencies, expressed as fractions, decimal amounts, or percentages of the whole data set

In the relative frequency table we explored, there are three flower types: Daisy, Rose, Violet.

Daisy has a group of 5 tally marks, a frequency of 5, and a relative frequency of $\frac{5}{25}$.

Rose has a group of 5 tally marks and 3 individual tally marks, a frequency of 8 and a relative frequency of $\frac{8}{25}$.

Violet has two groups of 5 tally marks and 2 individual tall mark, a frequency of 12, and a relative frequency of $\frac{12}{25}$.

The total frequency is 25 and has a relative frequency of $\frac{25}{25}$.

Collecting and organizing your own data

Let’s organize data.

Roll a pair of dice 30 times. You can use a digital dice. You can also use the data provided rather than collecting your own. Record the sum of each turn using a method of your choice.

Below is an example of the sum of numbers that you might collect after rolling a pair of dice 30 times.

Once you have recorded the results for all 30 trials, organize the data. Use a relative frequency table and one or two other methods that we have explored (stem-and-leaf plot or frequency table). Or you can create a detailed written or audio recording discussing the data.

• What method of data organization did you find most useful? Record your ideas using the method of your choice.
• Examine your relative frequency table. What sums occurred most often? What sums occurred least often?

Defining moments

For each item, select the corresponding definition.

Practice making relative frequency tables

Complete the Making Relative Frequency Tables in your notebook or use the following fillable activity document. Also, you can record your thoughts using an audio recording.

Reflection questions

Use the following questions to reflect on the different ways we can organize data. Record your responses.

• How could a relative frequency table be used to help us make predictions about data?
• Why do you think a relative frequency table might be a more useful way to organize data than a regular frequency table or a stem-and-leaf plot?
• When might a sports statistician use a relative frequency table?

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.