A teacher is analysing the study habits of students. The number of hours that students studied per week over 10 weeks is: 12, 15, 14, 10, 16, 20, 18, 17, 13, 11. Calculate the mean and standard deviat

$$\text{Mean} (\bar{x}) = \frac{\sum x_i}{n} = \frac{146}{10} = 14.6$$

The mean number of study hours per week is $\boxed{\text{14.6 hours}}$.

$$(12-14.6)^2 = (-2.6)^2 = 6.76$$ $$(15-14.6)^2 = (0.4)^2 = 0.16$$ $$(14-14.6)^2 = (-0.6)^2 = 0.36$$ $$(10-14.6)^2 = (-4.6)^2 = 21.16$$ $$(16-14.6)^2 = (1.4)^2 = 1.96$$ $$(20-14.6)^2 = (5.4)^2 = 29.16$$ $$(18-14.6)^2 = (3.4)^2 = 11.56$$ $$(17-14.6)^2 = (2.4)^2 = 5.76$$ $$(13-14.6)^2 = (-1.6)^2 = 2.56$$ $$(11-14.6)^2 = (-3.6)^2 = 12.96$$

$$s = \sqrt{10.04} \approx 3.16859$$

The standard deviation of the study hours is approximately $\boxed{\text{3.17 hours}}$.

$$(3-7)^2 = (-4)^2 = 16$$ $$(5-7)^2 = (-2)^2 = 4$$ $$(7-7)^2 = (0)^2 = 0$$ $$(9-7)^2 = (2)^2 = 4$$ $$(11-7)^2 = (4)^2 = 16$$

$$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N} = \frac{40}{5} = 8$$

The population variance is $\boxed{\text{8}}$.

16. For the dataset: 2, 4, 6, 8, 10, 12, find Q1 and Q3.
The dataset is already sorted: 2, 4, 6, 8, 10, 12. There are $n=6$ data points.

Since there are 6 data points (an even number), the median is the average of the 3rd and 4th values.

$$Q_2 = \frac{6 + 8}{2} = 7$$

$Q_1$ is the median of the lower half of the data. The lower half is 2, 4, 6.
The median of (2, 4, 6) is the middle value, which is 4.

$$Q_1 = 4$$

$Q_3$ is the median of the upper half of the data. The upper half is 8, 10, 12.
The median of (8, 10, 12) is the middle value, which is 10.

$$Q_3 = 10$$

The first quartile ($Q_1$) is $\boxed{\text{4}}$ and the third quartile ($Q_3$) is $\boxed{\text{10}}$.