Understanding the Range

What is the Range?

The range is a way to find out how spread out a set of numbers is. To calculate the range, you subtract the smallest number from the largest number in your data set.

How to Calculate the Range

  1. Find the largest number in your set.
  2. Find the smallest number in your set.
  3. Subtract the smallest number from the largest number.

Example of the Range

Let’s say we have the following numbers:

3, 7, 2, 9, 5

  1. The largest number is 9.
  2. The smallest number is 2.
  3. Now, subtract:$$ 9 – 2 = 7 $$

So, the range of these numbers is 7.

Understanding the Mode

What is the Mode?

The mode is the number that appears most often in a set of numbers. There can be one mode, more than one mode, or no mode at all if no number repeats.

How to Find the Mode

  1. List the numbers in your set.
  2. Count how many times each number appears.
  3. The number that appears the most is the mode.

Example of the Mode

Consider this set of numbers:

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

  1. The number 4 appears three times.
  2. The number 1 appears once.
  3. The number 2 appears twice.
  4. The number 3 appears once.

So, the mode is 4 because it appears the most often.

Key Rules to Remember

  • Range is found by subtracting the smallest number from the largest.
  • The mode is the number that occurs most frequently.
  • If all numbers occur the same number of times, there is no mode.
  • A set can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).

Tips and Tricks

  • Write numbers in order to make it easier to find the smallest and largest.
  • Use a tally chart to help keep track of how many times each number appears when finding the mode.
  • Practice with different sets of numbers to get comfortable with finding the range and mode.

Questions to Practice

Easy Level Questions

  1. What is the range of these numbers: 2, 4, 6, 8?
  2. Find the mode of this set: 3, 3, 4, 5, 6.
  3. Calculate the range: 1, 5, 9, 12.
  4. What is the mode of this set: 2, 4, 4, 6, 7?
  5. What is the range of these numbers: 10, 15, 20, 25?
  6. Find the mode: 8, 8, 9, 10, 10, 10.
  7. What is the range of these numbers: 5, 7, 10?
  8. What is the mode of this set: 1, 1, 1, 2, 3, 3?
  9. Calculate the range: 3, 3, 5, 5, 6.
  10. What is the mode of these numbers: 1, 2, 2, 3, 4, 4?

Medium Level Questions

  1. What is the range of these numbers: 4, 8, 10, 15, 20?
  2. Find the mode of this set: 3, 5, 5, 7, 9, 9, 10.
  3. Calculate the range: 12, 15, 18, 20, 25.
  4. What is the mode of this set: 11, 11, 12, 13, 14, 14, 14?
  5. What is the range of these numbers: 0, -5, 5, 10?
  6. Find the mode: 6, 7, 7, 8, 9, 9, 9.
  7. What is the range of these numbers: 1, 2, 4, 8, 16?
  8. What is the mode of this set: 20, 20, 21, 22, 23, 23, 23?
  9. Calculate the range: 14, 16, 18, 20, 25.
  10. What is the mode of these numbers: 5, 5, 6, 7, 8, 8, 9, 10?

Hard Level Questions

  1. What is the range of this set: -3, 0, 3, 6, 9, 12?
  2. Find the mode of this set: 5, 5, 6, 7, 8, 8, 10, 10, 10.
  3. Calculate the range: 25, 30, 35, 40, 50, 60.
  4. What is the mode of this set: 4, 4, 5, 5, 5, 6, 6, 7, 8?
  5. What is the range of these numbers: 100, 200, 300, 400?
  6. Find the mode: 15, 15, 16, 18, 18, 19, 20, 20.
  7. What is the range of these numbers: 1.5, 2, 2.5, 3, 3.5?
  8. What is the mode of this set: 12, 12, 13, 14, 15, 15, 15, 16, 17?
  9. Calculate the range: 45, 50, 55, 60, 65, 70.
  10. What is the mode of these numbers: 7, 7, 8, 9, 9, 10, 10, 11, 11?

Answers to Questions

Easy Level Answers

  1. 6
  2. 3
  3. 11
  4. 4
  5. 15
  6. 10
  7. 5
  8. 1
  9. 3
  10. 2

Medium Level Answers

  1. 16
  2. 5 and 9
  3. 13
  4. 14
  5. 15
  6. 9
  7. 15
  8. 23
  9. 11
  10. 5 and 8

Hard Level Answers

  1. 15
  2. 10
  3. 35
  4. 5
  5. 300
  6. 15 and 20
  7. 1.5
  8. 15
  9. 25
  10. 7 and 10

Feel free to ask questions if you’re unsure about anything! Keep practicing!