Integrated Math 1 / Unit 7: Descriptive Statistics
7.2 Standard Deviation and Spread
Notes
Standard deviation measures how far data values typically are from the mean. A larger standard deviation means more spread.
- If all values are equal, the standard deviation is 0.
- Adding the same number to every value changes the mean but not the standard deviation.
- Multiplying every value by a positive number $k$ multiplies the mean and standard deviation by $k$.
- Example: mean 70 and standard deviation 5. Most values lie within one standard deviation of the mean, between 65 and 75.
Practice
Two classes have the same mean score of 80. Class A scores range from 78 to 82. Class B scores range from 50 to 100. Which statement is true?
Class B's scores are spread farther from the mean.
What is the standard deviation of the data $7, 7, 7, 7, 7$?
Every value equals the mean, so no value is away from the mean.
A test has mean 70 and standard deviation 5. Which score is within one standard deviation of the mean?
Within one standard deviation means between $70 - 5 = 65$ and $70 + 5 = 75$. Only 73 is in that interval.
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