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Dot Plots: Standard Deviation — Easy Worksheet 2
Grade 10 · Whoobee Name: ____________________ Date: __________
Find the population standard deviation: divide the sum of the squared differences from the mean by n, the number of values, then take the square root. Round to the nearest tenth.
How to solve
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Example
The dot plot shows the number of minutes the bus was late for 5 days. Each dot stands for one day. The same data as a list: S = [9, 8, 10, 11, 7]. The mean is 9. What is the population standard deviation of the data?
Answer: 1.4
Not quite. The answer is
💡 Subtract the mean 9 from each value: 3, 1, 0, −3, −1, 0. Square each difference: 9, 1, 0, 9, 1, 0. Add the squares: 9 + 1 + 0 + 9 + 1 + 0 = 20. Variance = 20 ÷ 6 ≈ 3.333. Standard deviation = √3.333 = 1.826…, which rounds to 1.8.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 9 from each value: 3, 1, 0, −3, −1, 0. Square each difference: 9, 1, 0, 9, 1, 0. Add the squares: 9 + 1 + 0 + 9 + 1 + 0 = 20. Variance = 20 ÷ 6 ≈ 3.333. Standard deviation = √3.333 = 1.826…, which rounds to 1.8.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of push-ups done in one minute for 5 students. Each dot stands for one student. The same data as a list: S = [24, 21, 26, 23, 26]. The mean is 24. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 9 from each value: −2, −2, 2, 1, 1. Square each difference: 4, 4, 4, 1, 1. Add the squares: 4 + 4 + 4 + 1 + 1 = 14. Variance = 14 ÷ 5 = 2.8. Standard deviation = √2.8 = 1.673…, which rounds to 1.7.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 9 from each value: −2, −2, 2, 1, 1. Square each difference: 4, 4, 4, 1, 1. Add the squares: 4 + 4 + 4 + 1 + 1 = 14. Variance = 14 ÷ 5 = 2.8. Standard deviation = √2.8 = 1.673…, which rounds to 1.7.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of books read over the summer for 5 students. Each dot stands for one student. The same data as a list: S = [9, 10, 9, 9, 13]. The mean is 10. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 6 from each value: 2, 0, 0, −3, −2, 3. Square each difference: 4, 0, 0, 9, 4, 9. Add the squares: 4 + 0 + 0 + 9 + 4 + 9 = 26. Variance = 26 ÷ 6 ≈ 4.333. Standard deviation = √4.333 = 2.082…, which rounds to 2.1.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 6 from each value: 2, 0, 0, −3, −2, 3. Square each difference: 4, 0, 0, 9, 4, 9. Add the squares: 4 + 0 + 0 + 9 + 4 + 9 = 26. Variance = 26 ÷ 6 ≈ 4.333. Standard deviation = √4.333 = 2.082…, which rounds to 2.1.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of text messages sent in one hour for 6 teens. Each dot stands for one teen. The same data as a list: S = [15, 13, 15, 11, 10, 14]. The mean is 13. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 8 from each value: 0, 3, −2, −1, 2, −2. Square each difference: 0, 9, 4, 1, 4, 4. Add the squares: 0 + 9 + 4 + 1 + 4 + 4 = 22. Variance = 22 ÷ 6 ≈ 3.667. Standard deviation = √3.667 = 1.915…, which rounds to 1.9.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 8 from each value: 0, 3, −2, −1, 2, −2. Square each difference: 0, 9, 4, 1, 4, 4. Add the squares: 0 + 9 + 4 + 1 + 4 + 4 = 22. Variance = 22 ÷ 6 ≈ 3.667. Standard deviation = √3.667 = 1.915…, which rounds to 1.9.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of minutes the bus was late for 5 days. Each dot stands for one day. The same data as a list: S = [10, 11, 10, 11, 13]. The mean is 11. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 3 from each value: 2, 0, 1, 0, 0, −3. Square each difference: 4, 0, 1, 0, 0, 9. Add the squares: 4 + 0 + 1 + 0 + 0 + 9 = 14. Variance = 14 ÷ 6 ≈ 2.333. Standard deviation = √2.333 = 1.528…, which rounds to 1.5.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 3 from each value: 2, 0, 1, 0, 0, −3. Square each difference: 4, 0, 1, 0, 0, 9. Add the squares: 4 + 0 + 1 + 0 + 0 + 9 = 14. Variance = 14 ÷ 6 ≈ 2.333. Standard deviation = √2.333 = 1.528…, which rounds to 1.5.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of rainy days for 5 months. Each dot stands for one month. The same data as a list: S = [6, 2, 3, 7, 2]. The mean is 4. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 24 from each value: −1, 2, −3, 2, 0, 0. Square each difference: 1, 4, 9, 4, 0, 0. Add the squares: 1 + 4 + 9 + 4 + 0 + 0 = 18. Variance = 18 ÷ 6 = 3. Standard deviation = √3 = 1.732…, which rounds to 1.7.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 24 from each value: −1, 2, −3, 2, 0, 0. Square each difference: 1, 4, 9, 4, 0, 0. Add the squares: 1 + 4 + 9 + 4 + 0 + 0 = 18. Variance = 18 ÷ 6 = 3. Standard deviation = √3 = 1.732…, which rounds to 1.7.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of hours of sleep for 5 students. Each dot stands for one student. The same data as a list: S = [5, 10, 11, 11, 8]. The mean is 9. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 15 from each value: −1, 2, 0, −2, 0, 1. Square each difference: 1, 4, 0, 4, 0, 1. Add the squares: 1 + 4 + 0 + 4 + 0 + 1 = 10. Variance = 10 ÷ 6 ≈ 1.667. Standard deviation = √1.667 = 1.291…, which rounds to 1.3.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 15 from each value: −1, 2, 0, −2, 0, 1. Square each difference: 1, 4, 0, 4, 0, 1. Add the squares: 1 + 4 + 0 + 4 + 0 + 1 = 10. Variance = 10 ÷ 6 ≈ 1.667. Standard deviation = √1.667 = 1.291…, which rounds to 1.3.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of text messages sent in one hour for 5 teens. Each dot stands for one teen. The same data as a list: S = [16, 10, 10, 16, 13]. The mean is 13. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract the mean 12 from each value: −2, 2, 1, 2, −3. Square each difference: 4, 4, 1, 4, 9. Add the squares: 4 + 4 + 1 + 4 + 9 = 22. Variance = 22 ÷ 5 = 4.4. Standard deviation = √4.4 = 2.098…, which rounds to 2.1.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 12 from each value: −2, 2, 1, 2, −3. Square each difference: 4, 4, 1, 4, 9. Add the squares: 4 + 4 + 1 + 4 + 9 = 22. Variance = 22 ÷ 5 = 4.4. Standard deviation = √4.4 = 2.098…, which rounds to 2.1.
💡 How to solve: Dot Plots: Standard Deviation
Step 1: find the mean. Step 2: subtract the mean from each value and square the difference. Step 3: add the squares and divide by n to get the variance. Step 4: take the square root. Example: S = [2, 4, 4, 6] has mean 4. The squared differences are 4, 0, 0, 4, which add to 8. Variance = 8 ÷ 4 = 2 and standard deviation = √2 ≈ 1.4.
Try a similar one
The dot plot shows the number of books read over the summer for 5 students. Each dot stands for one student. The same data as a list: S = [9, 10, 9, 14, 8]. The mean is 10. What is the population standard deviation of the data?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Dot Plots: Standard Deviation — Easy Worksheet 2
Find the population standard deviation: divide the sum of the squared differences from the mean by n, the number of values, then take the square root. Round to the nearest tenth.