Mean and Standard Deviation

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1. 1. The data0:00
   $$2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9$$

   $n = 8$ values

2. 2. Mean0:11
   1. $$\bar{x} = \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8}$$
   2. $$\bar{x} = \frac{40}{8} = 5$$
3. 3. Squared deviations0:19
   1. $$(x - \bar{x})^2:\ 9,\ 1,\ 1,\ 1,\ 0,\ 0,\ 4,\ 16$$
   2. $$\sum (x - \bar{x})^2 = 32$$
4. 4. Standard deviation0:31
   1. $$\sigma = \sqrt{\frac{32}{8}} = \sqrt{4} = 2$$
      population
   2. $$s = \sqrt{\frac{32}{7}} \approx 2.14$$
      sample
5. 5. Recap0:46
   • ✓Mean: add, then divide by $n$.
   • ✓Square the deviations, add them up.
   • ✓Divide by $n$ (population) or $n - 1$ (sample), then take the square root.

Mean, median, mode, variance and standard deviation.

• Mean Median Mode Calculator: try the same kind of problem with your own numbers.
• Standard Deviation Calculator: try the same kind of problem with your own numbers.
• More statistics practice problems
• Descriptive Statistics Study Guide (study guide)
• AP Statistics Unit 1: Exploring One-Variable Data: the AP unit this lesson supports.
• Statistics calculators and topics
• Step-by-step solver: check your own answer with hints.

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