Standard Deviation Worksheet
Calculate population standard deviation and interpret consistency. Includes a worked example, printable practice, and an answer key with explanations.
The answer key follows the practice below. In the editor, remove the final answer-key section before sharing a student copy.
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Standards
Topics
Standard Deviation Practice
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Learning goal and worked example
Calculate population standard deviation and interpret consistency.
For {2,2,4,4}, the mean is 3 and population variance is (1+1+1+1)/4 = 1. Standard deviation is √1 = 1, in the original units.
Extension: requires the mean, squares, and square roots. Check your local Grade 9 syllabus.
Read each question carefully and provide your answers. Show all your work for calculation problems.
1. Standard deviation is a measure of the of a data set from its mean.
2. A small standard deviation indicates that data points are generally to the mean.
3. The square of the standard deviation is called the .
4. Calculate the mean of the following data set: {2, 4, 6, 8, 10}.
5. Treat {2, 4, 6, 8, 10} as the complete population. Calculate its population standard deviation, dividing the sum of squared deviations by N = 5 before taking the square root. Round to two decimal places.
6. Which of the following data sets would likely have the largest standard deviation?
{5, 5, 5, 5, 5}
{1, 2, 3, 4, 5}
{1, 5, 10, 15, 20}
{4, 5, 6, 7, 8}
7. A standard deviation of zero means all data points are identical.
True
False
8. The standard deviation can be a negative value.
True
False
9. Two classes took the same math test. Class A had a mean score of 75 with a standard deviation of 5. Class B had a mean score of 75 with a standard deviation of 12. Which class had more consistent scores? Explain your reasoning.
Answer key and worked solutions
1. Spread (or dispersion). 2. Close. 3. Variance.
4. Mean = (2+4+6+8+10)/5 = 6.
5. Squared deviations sum to 40. Population variance = 40/5 = 8; population standard deviation = √8 ≈ 2.83. Using n−1 would answer a different, sample-statistics question.
6. c: {1,5,10,15,20}. Its population variance is 46.16, compared with 0,2,2 for the other options.
7. True. Every squared deviation must be zero. 8. False. A square root of a nonnegative variance cannot be negative.
9. Class A is more consistent: standard deviation 5 is less than 12, so scores are less dispersed around the shared mean of 75.
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