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ਕਦਮ ਦਰ ਕਦਮ

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, 4, 4, 4, 5, 5, 7, 9

   Sort the values.

4. \text{median} = \frac{9}{2}

   The middle value (or the mean of the two middle values).

5. 4

   Mode: the most frequent value (appears 3 times).

6. \text{range} = 9 - 2 = 7

   Range: largest minus smallest.

7. (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.

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

   Population variance (divide by n).

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

   Sample variance (divide by n − 1).

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

    Standard deviation is the square root of the variance.