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Dot Plots: Standard Deviation — Easy Worksheet 1
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 23 from each value: −2, 1, 2, −1, −2, 2. Square each difference: 4, 1, 4, 1, 4, 4. Add the squares: 4 + 1 + 4 + 1 + 4 + 4 = 18. Variance = 18 ÷ 6 = 3. Standard deviation = √3 = 1.732…, which rounds to 1.7.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 23 from each value: −2, 1, 2, −1, −2, 2. Square each difference: 4, 1, 4, 1, 4, 4. Add the squares: 4 + 1 + 4 + 1 + 4 + 4 = 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 points scored for 6 games. Each dot stands for one game. The same data as a list: S = [21, 24, 23, 24, 19, 21]. The mean is 22. 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, −1, −1, 1, 0. Square each difference: 1, 4, 1, 1, 1, 0. Add the squares: 1 + 4 + 1 + 1 + 1 + 0 = 8. Variance = 8 ÷ 6 ≈ 1.333. Standard deviation = √1.333 = 1.155…, which rounds to 1.2.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 15 from each value: −1, 2, −1, −1, 1, 0. Square each difference: 1, 4, 1, 1, 1, 0. Add the squares: 1 + 4 + 1 + 1 + 1 + 0 = 8. Variance = 8 ÷ 6 ≈ 1.333. Standard deviation = √1.333 = 1.155…, which rounds to 1.2.
💡 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 6 students. Each dot stands for one student. The same data as a list: S = [8, 9, 9, 8, 6, 8]. The mean is 8. 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: 0, −1, 0, −1, 2. Square each difference: 0, 1, 0, 1, 4. Add the squares: 0 + 1 + 0 + 1 + 4 = 6. Variance = 6 ÷ 5 = 1.2. Standard deviation = √1.2 = 1.095…, which rounds to 1.1.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 12 from each value: 0, −1, 0, −1, 2. Square each difference: 0, 1, 0, 1, 4. Add the squares: 0 + 1 + 0 + 1 + 4 = 6. Variance = 6 ÷ 5 = 1.2. Standard deviation = √1.2 = 1.095…, which rounds to 1.1.
💡 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 rainy days for 5 months. Each dot stands for one month. The same data as a list: S = [7, 8, 11, 9, 10]. 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 25 from each value: 1, 1, 2, −3, −1. Square each difference: 1, 1, 4, 9, 1. Add the squares: 1 + 1 + 4 + 9 + 1 = 16. Variance = 16 ÷ 5 = 3.2. Standard deviation = √3.2 = 1.789…, which rounds to 1.8.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 25 from each value: 1, 1, 2, −3, −1. Square each difference: 1, 1, 4, 9, 1. Add the squares: 1 + 1 + 4 + 9 + 1 = 16. Variance = 16 ÷ 5 = 3.2. Standard deviation = √3.2 = 1.789…, 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 text messages sent in one hour for 5 teens. Each dot stands for one teen. The same data as a list: S = [17, 15, 16, 14, 18]. The mean is 16. 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, 2, −2, 2. Square each difference: 4, 0, 4, 4, 4. Add the squares: 4 + 0 + 4 + 4 + 4 = 16. Variance = 16 ÷ 5 = 3.2. Standard deviation = √3.2 = 1.789…, which rounds to 1.8.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 6 from each value: −2, 0, 2, −2, 2. Square each difference: 4, 0, 4, 4, 4. Add the squares: 4 + 0 + 4 + 4 + 4 = 16. Variance = 16 ÷ 5 = 3.2. Standard deviation = √3.2 = 1.789…, 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 high temperature in °C for 6 days. Each dot stands for one day. The same data as a list: S = [24, 20, 24, 25, 25, 20]. The mean is 23. 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 26 from each value: 1, 1, −3, 1, 0. Square each difference: 1, 1, 9, 1, 0. Add the squares: 1 + 1 + 9 + 1 + 0 = 12. Variance = 12 ÷ 5 = 2.4. Standard deviation = √2.4 = 1.549…, which rounds to 1.5.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 26 from each value: 1, 1, −3, 1, 0. Square each difference: 1, 1, 9, 1, 0. Add the squares: 1 + 1 + 9 + 1 + 0 = 12. Variance = 12 ÷ 5 = 2.4. Standard deviation = √2.4 = 1.549…, 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 push-ups done in one minute for 6 students. Each dot stands for one student. The same data as a list: S = [23, 24, 25, 22, 26, 24]. 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 12 from each value: −1, 0, 2, 0, −1. Square each difference: 1, 0, 4, 0, 1. Add the squares: 1 + 0 + 4 + 0 + 1 = 6. Variance = 6 ÷ 5 = 1.2. Standard deviation = √1.2 = 1.095…, which rounds to 1.1.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 12 from each value: −1, 0, 2, 0, −1. Square each difference: 1, 0, 4, 0, 1. Add the squares: 1 + 0 + 4 + 0 + 1 = 6. Variance = 6 ÷ 5 = 1.2. Standard deviation = √1.2 = 1.095…, which rounds to 1.1.
💡 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 goals scored for 5 matches. Each dot stands for one match. The same data as a list: S = [4, 1, 4, 4, 2]. The mean is 3. 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: 2, −2, 0, 0, 2, −2. Square each difference: 4, 4, 0, 0, 4, 4. Add the squares: 4 + 4 + 0 + 0 + 4 + 4 = 16. Variance = 16 ÷ 6 ≈ 2.667. Standard deviation = √2.667 = 1.633…, which rounds to 1.6.
✓ Correct!
Not quite. The answer is
💡 Subtract the mean 8 from each value: 2, −2, 0, 0, 2, −2. Square each difference: 4, 4, 0, 0, 4, 4. Add the squares: 4 + 4 + 0 + 0 + 4 + 4 = 16. Variance = 16 ÷ 6 ≈ 2.667. Standard deviation = √2.667 = 1.633…, which rounds to 1.6.
💡 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 quiz score for 5 students. Each dot stands for one student. The same data as a list: S = [7, 5, 6, 9, 8]. The mean is 7. 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 1
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.