After the lesson of yesterday - Collecting data - we can now move on to organizing data.

An example of a frequency table

Organizing data

The data that we collect is called the raw data.  This data has not yet been organized or summarized.  The lists of data that we collect, can be difficult to read, think of having 20 questionnaires, each with different answers.  To make it easier we organize this data.  For grade 7 learners, we are going to organize this data in frequency tables (tally tables) and stem-and-leaf displays.

An example of a stem-and-leaf display

A frequency table has 3 columns, the first column is for the data values, the 2nd column for the tallies and the 3rd column for the frequency (Total)

Tallies are counting marks that are grouped in bunches of five:  llll

We can use the following as an example:

A hockey coach kept a record of her team's scores during the season.  The team played 10 matches. Here is her data:

2; 4; 1; 2; 1; 1; 1; 4; 2; 0

She organized the data into a frequency table:

The data in the frequency table shows us the scores the team made for the season.  They scored 1 goal in 4 matches, 2 goals in 3 matches, and 4 goals in two of the matches.  We can also see that there was no match where they scored 3 goals and 1 match where they had no goals.   If we add all the tallies together, it will be equal to 10.  In the data she gave us, she said they played 10 matches during the season.

Another way to organize data is in a stem-and-leaf display

A stem-and-leaf display is a useful way to organize numerical data of which the values have more than 1 digit.  We break the data up into a stem and a leaf part.  We choose the values of the stem in a way that the leaf column consists of a single digit.

Below are the ages of 30 people living in a village:

 

The first heading of the column is the stem:  the stem is the tens of each number.  You will see there is also a 0, which means that those people haven't reached the age of 10 yet, they are still under the age of 10, a single digit.  To work out which numbers you have to use in the stem, you take, in this case, the oldest and the youngest age, the oldest age was 92 and the youngest age only 8.

This means that the numbers in the stem must go from 0 to 9.

After I know which numbers to put in the stem column, I can start writing the rest of the data in the leaf column.

The leaf is what is left of the number.  You will see where the stem is 1, the numbers in the leaf is 3;4;0;7 and 9

If I put these numbers together, I will get 13, 14, 10, 17 and 19

The stem is the tens of the digit and the leaf is the units.

This carries on for the stem of 2 to 9.  If you put the numbers back together you will have a two digit number.

Always tell your learners to arrange the data from small to big or big to small.  For the next lesson, this data that is arranged will help a lot with what we are going to do. 

They can add a column on the right to arrange the data.  The information will still be the same, the data has just been arranged from small to big.