แก้ไขปัญหาคณิตศาสตร์

ก้าวต่อก้าว

1. 12, 15, 11, 18, 14

   5 values.

2. \bar{x} = \frac{12 + 15 + 11 + 18 + 14}{5} = \frac{70}{5} = 14

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

3. 11, 12, 14, 15, 18

   Sort the values.

4. \text{median} = 14

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

5. \text{none}

   Mode: the most frequent value (none repeats).

6. \text{range} = 18 - 11 = 7

   Range: largest minus smallest.

7. (12 - 14)^2 = 4 ,\; (15 - 14)^2 = 1 ,\; (11 - 14)^2 = 9 ,\; (18 - 14)^2 = 16 ,\; (14 - 14)^2 = 0

   Squared deviations from the mean.

8. \sigma^2 = \frac{\sum (x_i - \bar x)^2}{n} = 6

   Population variance (divide by n).

9. s^2 = \frac{\sum (x_i - \bar x)^2}{n - 1} = \frac{15}{2}

   Sample variance (divide by n − 1).

10. \sigma = \sqrt{6} = \sqrt{6} \approx 2.4495,\quad s = \frac{\sqrt{30}}{2} \approx 2.7386

    Standard deviation is the square root of the variance.