Center and Variability

Grade 6 · measurement · 100 practice problems · read aloud

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📊 Center and Variability

What is it and Why is it Useful?

Center and variability are ways to describe a set of data. The center is a single number that represents a "typical" value (like an average). Variability describes how spread out the data is. This helps us summarize data quickly and compare different sets of data to see which is more consistent.

How to Find Center and Variability

  1. Find the Mean (Average): Add all the numbers together, then divide by how many numbers there are. This is a measure of center.
  2. Find the Median: Put the numbers in order from least to greatest. The median is the middle number. This is another measure of center.
  3. Find the Range: Subtract the smallest number from the largest number. This is a measure of variability.

Worked Examples

Example 1: Test Scores
Data: 85, 90, 78, 92, 85

  1. Mean: (85 + 90 + 78 + 92 + 85) ÷ 5 = 430 ÷ 5 = 86
  2. Median: Order: 78, 85, 85, 90, 92. The middle number is 85.
  3. Range: 92 - 78 = 14

✅ The typical score is about 86, and the scores are spread out by 14 points.

Example 2: Height of Seedlings (in cm)
Data: 10, 15, 22, 18, 14

  1. Mean: (10 + 15 + 22 + 18 + 14) ÷ 5 = 79 ÷ 5 = 15.8 cm
  2. Median: Order: 10, 14, 15, 18, 22. The middle number is 15 cm.
  3. Range: 22 - 10 = 12 cm

⚠️ Common Mistakes

  • Forgetting to order numbers for the median. Always put your data in order first!
  • Mixing up mean and median. Remember, "mean" is the "average," and "median" is the "middle."
  • Calculating range incorrectly. It's always Largest - Smallest. Don't get the order wrong!

💡 Tips & Tricks

  • Memory Aid: The "mean" teacher is "average." The "median" strip is in the "middle" of the road.
  • Check your mean: Your mean should be somewhere between the smallest and largest numbers in your data set.
  • If two data sets have a similar mean, the one with the smaller range is more consistent.

How to Practice

  • Use data from your life! Find the mean, median, and range of your homework scores, or how many minutes you spend on chores each day.
  • Ask a family member for 5 numbers and calculate the measures of center and variability for them.
  • Practice with online math games that focus on data and statistics.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 √(144 + 25) = ?

Hint: First perform the addition inside the square root, then find the square root of that result.

Show the answer

Answer: 13

  1. Look at the expression inside the square root: 144 + 25.
  2. Add the two numbers together. 144 + 25 = 169
  3. The problem now becomes the square root of the result from
  4. So we need to calculate the square root of 169.
  5. Recall that finding the square root means finding a number which, when multiplied by itself, gives the number inside the root. We ask: "What number multiplied by itself equals 169?"
  6. We know that 12 * 12 = 144, which is too small. We also know that 13 * 13 = 169.
  7. Since 13 * 13 = 169, the square root of 169 is 13. Therefore, the final answer is 13.

2 Find the mean of: 12, 15, 18, 21, 24

Hint: To find the mean, add all the numbers together and then divide by how many numbers there are. For example, for numbers 4, 6, and 8, you would calculate (4+6+8) ÷ 3.

Show the answer

Answer: 18

  1. Add all the numbers together. 12 + 15 = 27 27 + 18 = 45 45 + 21 = 66 66 + 24 = 90 The sum of all the numbers is 90.
  2. Count how many numbers are in the set. The numbers are: 12, 15, 18, 21, 24. There are 5 numbers in the set.
  3. Divide the sum by the count. Mean = (Sum of numbers) / (Count of numbers) Mean = 90 / 5
  4. Perform the division. 90 divided by 5 equals 18. Therefore, the mean of the numbers 12, 15, 18, 21, and 24 is 18.

To find the mean of a set of numbers, follow these steps:

3 Find the mean of: 24, 31, 29, 26, 34

Hint: To find the mean, add all the numbers together and then divide by how many numbers there are. For example, for numbers 10, 20, and 30, you would calculate (10 + 20 + 30) ÷ 3.

Show the answer

Answer: 28.8

  1. Add all the numbers together: 24 + 31 + 29 + 26 + 34 = 144
  2. Count how many numbers there are: There are 5 numbers.
  3. Divide the sum by the number of items: 144 ÷ 5 = 28.8 The mean is 28.8.

4 The mean of 12, 15, 18, 21, and 24 is ?

Hint: To find the mean, add all the numbers together and then divide by how many numbers there are. For example, the mean of 5, 10, and 15 is found by adding them to get 30, then dividing by 3 to get 10.

Show the answer

Answer: 18

  1. Identify the numbers given in the problem. The numbers are: 12, 15, 18, 21, and 24.
  2. Recall that the mean (average) is calculated by adding all the numbers together and then dividing by how many numbers there are.
  3. Add all the numbers. 12 + 15 = 27 27 + 18 = 45 45 + 21 = 66 66 + 24 = 90 So, the total sum is 90.
  4. Count how many numbers there are. We have 5 numbers: 12, 15, 18, 21, 24.
  5. Divide the total sum by the number of numbers. Mean = 90 / 5 = 18.
  6. Conclusion. The mean of the numbers 12, 15, 18, 21, and 24 is 18.

5 Find the mean of: 15, 22, 18, 25, 20 = ?

Hint: To find the mean, add all the numbers together and then divide by how many numbers there are. For example, the mean of 10, 20, and 30 is found by adding them to get 60, then dividing by 3.

Show the answer

Answer: 20

  1. Add all the numbers together. 15 + 22 = 37 37 + 18 = 55 55 + 25 = 80 80 + 20 = 100 So, the sum of all the numbers is 100.
  2. Count how many numbers are in the set. The numbers are: 15, 22, 18, 25, 20. We count 5 numbers.
  3. Divide the sum by the count of numbers. Mean = (Sum of numbers) / (Count of numbers) Mean = 100 / 5
  4. Perform the division. 100 divided by 5 equals 20. Therefore, the mean of the numbers 15, 22, 18, 25, and 20 is 20.

To find the mean of a set of numbers, we follow these steps:

6 Find the mean of: 24, 31, 29, 36, 40 = ?

Hint: To find the mean, add all the numbers together and then divide by how many numbers there are. For example, for numbers 10, 20, and 30, you would calculate (10 + 20 + 30) ÷ 3.

Show the answer

Answer: 32

  1. Add all the numbers together: 24 + 31 + 29 + 36 + 40 = 160.
  2. Count how many numbers there are: There are 5 numbers.
  3. Divide the sum by the number of items: 160 ÷ 5 = 32. The mean is 32.
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