Tables and diagrams (Tabeller och diagram)

Ämne / Topic

Frequency tables and calculating mean, medium, and mode.

Inlärningsmål / Learning Goals

Understand how to create a frequency table and how to calculate relative frequency

Understand the difference (and how to calculate) mean, median, and mode

Be able to find the range of a distribution

Google Slides & Videos

3. Aktiviteter / Key Activities

To better understand this concept, we need to look at all the parts that make it up and see how they all interact with one another.

The best way to understand this concept is going through examples and applying practices to solve them.

1. Frequency & Relative Frequency Tables

Steven and Renee are a husband and wife couple that just started a local restaurant business. They want to have a signature steak to serve on the weekends. They asked twenty of their friends to taste test five different types of steaks to see which steak they should serve. Four people choose steak number one, five people choose steak number two, two people choose steak number three, six people choose steak number four, and three people choose steak number five. Steven and Renee can use frequency and relative frequency tables to analyze and visualize their choices.

A frequency table is a chart that shows the popularity or mode of a certain type of data.When we look at a frequency, we are looking at the number of times an event occurs within a given scenario.

A relative frequency table is a chart that shows the popularity or mode of a certain type of data based on the population sampled. When we look at relative frequency, we are looking at the number of times a specific event occurs compared to the total number of events.

Creating Frequency Tables: Example 1

The data set for the steak tasting is as follows, where each number represents the steak that was chosen as the best:

1, 5, 3, 1, 2, 3, 4, 5, 1, 4, 2, 4, 4, 5, 1, 4, 2, 4, 2, 2

We can use our data to create a frequency table like this.

Notice that the first column indicates the type of steak.

The second column shows a tally mark indicating the number of people who chose each steak.

The third column indicates the frequency with which each steak was chosen. The tally mark and the frequency number should always match.

To create a relative frequency table, we need to do some dividing. A relative frequency table shows the number of people that chose each steak compared to the number of people that did the tasting.

Take a look at this new chart.

To find the relative frequency for each steak choice, we need to take the frequency for each choice and divide that number by 20.

We are dividing by 20 here because there was a total number of 20 people who tasted the steaks.

The number in the third column is the relative frequency number. To convert the relative frequency number to a percentage, it must be multiplied by 100.

2. Mean

Calculating the MEAN is finding the average of the data.

To do this, the following formula can be used:

If we continue with the example above, we can find the mean of the data in the following way:

m = 1+5+3+1+2+3+4+5+1+4+2+4+4+5+1+4+2+4+2+2

20

m = 59 / 20

m = 2.95

This means that the average steak is steak 3.

3. Mode

The MODE is the number or event that occurs most often.

So looking at the steak example, we can find the mode in the following way:

1, 5, 3, 1, 2, 3, 4, 5, 1, 4, 2, 4, 4, 5, 1, 4, 2, 4, 2, 2

1 = 4

2 = 5

3 = 2

4 = 6 (mode)

5 = 3

You can also find your mode, by looking at your frequency table.

4. Median

The MEDIAN is the middle term.

To find the median, all the data must be put into numerical order.

1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5

Once the data has been arranged in numerical order, start by cancelling the data from the outside in:

1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5

You continue cancelling out data until you are left with one, that is the median for the set of data.

For the example we are busy with, you will see that we have two numbers left, if that happens, you find the median in the following way:

a + b

2

So for the example that we are busy with, the median is:

3 + 3

2

= 3

5. Median

When calculating RANGE, take your lowest number and subtract it from your highest number.

So, if we look at the example that we are busy, you would find the range as follows:

1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5

5 - 1 = 4

The range is 4

6. Spreading

SPREADING refers to graphing the information.

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Once the example has been completed, students can answer 2 questions, to check that they understand the concept.

1. Pulse rate (per minute) of 25 persons were recorded as

61, 75, 71, 72, 70, 65, 77, 72, 67, 80, 77, 62, 71, 74, 79, 67, 80, 77, 62, 71, 74, 61, 70, 80, 72, 59, 78, 71, 72.

a. Construct a frequency table using the data.

b. Use the frequency table to construct a graph representing the data.

c. Calculate the mean, mode, median and range for the given data.

2. . The temperature in o F on 20 days during the month of June was as follows:

70 , 76, 76 , 74, 70, 70, 72, 74, 78, 80, 74, 74, 78 , 76, 78, 76, 74, 78, 80, 76

a. Construct a frequency table using the data.

b. Use the frequency table to construct a graph representing the data.

c. Calculate the mean, mode, median and range for the given data.

5. Stängning / Closure / Summary of lesson

Take up difficult problems from leveled questions on the board.