Lesson 28 — Activity 1: Range and Mode

Getting Ready

Have you ever been in a class where after a test, the teacher writes the highest and lowest marks on the board as well as the class average? If you have, you have already looked at some of the statistics you will cover in this lesson.

In this first activity, you will learn about these terms: range and mode.

This student is looking at the marks from a test.

One thing that you may have looked at without even thinking about it is the difference between the highest mark and the lowest mark. This is called the range. A range simply tells the distance between the highest and lowest numbers.

Let's use the numbers 50, 62, 48, 79, 63, 81, and 63. Whenever you are dealing with a statistics question, it is a good idea to put the numbers in order from lowest to highest before you do anything else.

50, 62, 48, 79, 63, 81, 63 ordered becomes: 48, 50, 62, 63, 63, 79, 81

Notice that there are two number 63s in the list. It is important that you list all of the numbers in your list, no matter how many times they appear.

To calculate the range, simply take the largest number in your list and subtract the smallest number from it. In this case, the largest number is 81 and the smallest is 48.

81 – 48 = 33

The range of the numbers is 33.

Try This:

This is Matt's second test this term.

Here is a list of Matt's exam marks for the first term. Find the range of the marks. (Remember to list the numbers in order from lowest to highest first.)

Test 1: 78

Test 2: 90

Test 3: 71

Test 4: 68

Test 5: 89

68, 71, 78, 89, 90
90 – 68 = 22
The range of the numbers is 22.

Another piece of statistical data that people like to know is the mode. The mode is the number that occurs the most often.

If you look at the example above, the mode would be 63 because it is the number that appears twice while all of the other numbers only appear once.

Let's look at another example: 6, 4, 7, 9, 2, 4, 7, 8

What is the mode of these numbers?

(Remember, the first thing to do is to put them in order.)

6, 4, 7, 9, 2, 4, 7, 8 ordered becomes: 2, 4, 4, 6, 7, 7, 8, 9

Notice that we have two different numbers that are repeated twice. There are two 4s and two 7s. Therefore the modes for this list of numbers is 4 and 7. You can have more than one mode for a set of numbers.

Try This:

This is one of Kat's tests this term.Find the mode for this set of Kat's marks:

67, 82, 99, 82, 88, 71, 78, 67

67, 67, 71, 78, 82, 82, 88, 99
The modes for this set of numbers are 67 and 82.

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