Measures of Center Frequency Lesson

Constructing Frequency Tables

Construct and Interpret a frequency table with suitable class intervals for discrete data 

Objectives

By the end of the lesson, you should be able to:

1. Correctly define key terms; frequency, data, discrete data, frequency table, class intervals.

2. Correctly record and construct a frequency table to represent given data.

3. Accurately determine the class interval for discrete data.

4. Accurately identify and interpret information from a given frequency table .

Definition of Key Terms

• A frequency table is a table that lists items and shows the number of times the items occur. We represent the frequency by the English alphabet ‘f’. 

• Frequency refers to the number of times an event or a value occurs. 

• Data is a collection of facts, such as numbers, words, measurements, observations or just descriptions of things.

• Discrete data is quantitative values that are countable and are represented by whole numbers.

Constructing Frequency tables

• Frequency tables can be constructed with two columns: The column for data values and the frequency; but its best recommended to use three (inclusion of tally marks).

• When the observations are large, it may not be easy to find the frequencies by simply counting.

• The use of tally marks makes it easier to keep track of the number of times a data value occurs.

• Using the tally makes it easier to represent the frequency of each data value.

Creating a frequency table

The marks awarded for an assignment set for a Year 8 class of 20 students were as follows:

    6    7    5    7    7    8    7    6    9    7

    4    10  6    8    8    9    5    6    4    8

Present this information in a frequency table.

Step 1: Make three columns. The first column carries the data values in ascending order (from lesser to large values). 

Creating a frequency table

Step 2: The second column contains the number of times the data value occurs using tally marks.

To complete the second column, go through the list of data values and place one tally mark at the appropriate place in the second column for every data value. When the fifth tally is reached for a mark, draw a horizontal line through the first four tally marks. We continue this process until all data values in the list are tallied.

Creating a frequency table

Step 3: Count the number of tally marks for each data value and write it in the third column. This represents the frequency for the data values in the set.

Fill in the Blanks

The

of a particular data value is the number of times the data value occurs.

Multiple Choice

Which score has the highest frequency?

• 7

• 6

• 5

• 8

Multiple Choice

What is the frequency for the number of students who own 2 pets?

• 3

• 7

• 6

• 5

Multiple Select

When constructing a frequency table you must have

• slides

• columns

• data values

• headings

Multiple Choice

What is the mode of the following data values?

• 3

• 2

• 4

• 1

Multiple Choice

What is the mean of the following data values?

• 8

• 7.9

• 8.1

• 7

Constructing Frequency tables for Group data

Determining class intervals

Challenge!!

How would you construct a frequency table for the following data values:

9,16,13,7,4,18,10,17,9,12,5,9,9,1,8,1,

10,5,11,15,6,14,9,1,12,5,8,15,14,17

Group (Class Intervals)

When the set of data values are spread out, it is difficult to set up a frequency table for every data value as there will be too many rows in the table. So we group the data into class intervals (or groups) to help us organize, interpret and analyze the data.

The frequency of a group (or class interval) is the number of data values that fall in the range specified by that group (or class interval).

Class Intervals

Let's try to group them, but what groups should we use?

To get started, put the numbers in order, then find the smallest and largest values in your data, and calculate the range (range = largest - smallest).

1,1,1,4,5,5,5,6,7,8,8,9,9,9,9,9,10,10,11,12,12,

13,14,14,15,15,16,17,17,18

The smallest value (the "minimum") is 1 cm

The largest value (the "maximum") is 18 cm

The range is 18−1 = 17 c

Group Size

Now calculate an approximate group size, by dividing the range by how many groups you would like.

Then round that group size up to some simple value (like 2 instead of 1.83 or 5 instead of 4.26).

Let us say we want about 5 groups.

Divide the range by 5:

17/5 = 3.4

Then round that up to 4

Pick a starting value that is less than or equal to the smallest value. Try to make it a multiple of the group size if you can.

Now calculate the list of groups. (We must go up to or past the largest value).

Starting at 0 and with a group size of 4 we get: 0, 4, 8, 12, 16.

Write down the groups.

Include the end value of each group that must be less than the next group.

The last group goes to 19 which is greater than the largest value. That is OK: the main thing is that it must include the largest value.

To complete the table, identify all data values that will be within each class intervals and write its frequency. 1,1,1,4,5,5,5,6,7,8,8,9,9,9,9,9,10,10,11,12,12,

13,14,14,15,15,16,17,17,18

Multiple Choice

What is the most popular pet?

• dog

• cat

• fish

• hamster

Multiple Choice

What is the frequency of the results from 20 to 29?

• 3

• 6

• 2

• 1

Multiple Choice

which of the following represents the group size given in the table?

• 1, 2, 3, 4, 5

• 0, 4, 6, 12, 16

• 0, 10, 20, 30, 40

• 0, 5, 10, 15, 20

Multiple Choice

The pass mark was 25, how many students do you think passed?

• 8

• 6

• 11

• 4