analyzing average wind patterns\nthe monthly wind speeds over a one - year period at denver international…

Explanation:

Step1: Arrange data in ascending order

9.6, 9.7, 9.9, 9.9, 10.0, 10.1, 10.1, 10.3, 10.7, 10.8, 11.0, 11.9

Step2: Calculate the median

Since there are 12 data - points (an even number), the median is the average of the 6th and 7th ordered values. Median=$\frac{10.1 + 10.1}{2}=10.1$

Step3: Calculate the mean

Mean=$\frac{9.6+9.7 + 9.9+9.9+10.0+10.1+10.1+10.3+10.7+10.8+11.0+11.9}{12}=\frac{123}{12}=10.25$

Step4: Calculate the population standard deviation

First, calculate the variance. The formula for population variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\mu)^{2}}{n}$, where $x_{i}$ are the data - points, $\mu$ is the mean, and $n$ is the number of data - points. $(9.6 - 10.25)^{2}=(-0.65)^{2}=0.4225$, $(9.7 - 10.25)^{2}=(-0.55)^{2}=0.3025$, $(9.9 - 10.25)^{2}=(-0.35)^{2}=0.1225$ (twice), $(10.0 - 10.25)^{2}=(-0.25)^{2}=0.0625$, $(10.1 - 10.25)^{2}=(-0.15)^{2}=0.0225$ (twice), $(10.3 - 10.25)^{2}=(0.05)^{2}=0.0025$, $(10.7 - 10.25)^{2}=(0.45)^{2}=0.2025$, $(10.8 - 10.25)^{2}=(0.55)^{2}=0.3025$, $(11.0 - 10.25)^{2}=(0.75)^{2}=0.5625$, $(11.9 - 10.25)^{2}=(1.65)^{2}=2.7225$ $\sum_{i = 1}^{12}(x_{i}-10.25)^{2}=0.4225+0.3025 + 2\times0.1225+0.0625+2\times0.0225+0.0025+0.2025+0.3025+0.5625+2.7225 = 5.04$ Variance $\sigma^{2}=\frac{5.04}{12}=0.42$ Population standard deviation $\sigma=\sqrt{0.42}\approx0.648$

Answer:

Median: 10.1 Mean: 10.25 Population standard deviation: 0.648