Математикалық тапсырмаларды шешу

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1. 2, 4, 4, 4, 5, 5, 7, 9

   8 values.

2. \bar{x} = \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = \frac{40}{8} = 5

   Mean: add them up and divide by how many there are.

3. (2 - 5)^2 = 9 ,\; (4 - 5)^2 = 1 ,\; (4 - 5)^2 = 1 ,\; (4 - 5)^2 = 1 ,\; (5 - 5)^2 = 0 ,\; (5 - 5)^2 = 0 ,\; \dots

   Squared deviations from the mean.

4. \sigma^2 = \frac{\sum (x_i - \bar x)^2}{n} = 4

   Population variance (divide by n).

5. s^2 = \frac{\sum (x_i - \bar x)^2}{n - 1} = \frac{32}{7}

   Sample variance (divide by n − 1).

6. \sigma = \sqrt{4} = 2,\quad s = \frac{4 \sqrt{14}}{7} \approx 2.1381

   Standard deviation is the square root of the variance.