Let's work through this step by step.

1. Distribution Type:

Looking at the data, the number of hate crimes fluctuates across the years. The data starts high in 2007, decreases in the middle years, and rises again towards 2017–2018. This distribution likely appears to have a skewed left pattern because the values decrease more dramatically in the middle years and rise again, leaving a longer left tail.

2. Mean:

The mean ($\mu$) is the average of the values, calculated by summing the total number of hate crimes and dividing by the number of years.

Hate Crime Data:

$\{7635, 7783, 6604, 6628, 6222, 5796, 5928, 5479, 5850, 6121, 7175, 7120\}$

First, sum these values: $7635 + 7783 + 6604 + 6628 + 6222 + 5796 + 5928 + 5479 + 5850 + 6121 + 7175 + 7120 = 81341$

Next, divide by the number of data points (12 years): $\mu = \frac{81341}{12} = 6778.42$

So, the mean number of hate crimes is approximately 6778.42.

3. Population Standard Deviation:

The population standard deviation ($\sigma$) measures the spread of data points. The formula for population standard deviation is:

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

Where:

• $x_i$ are the individual data points,
• $\mu$ is the mean,
• $N$ is the total number of data points (12 in this case).

Step-by-Step Calculation:

1. Subtract the mean from each data point and square the result.
2. Sum these squared differences.
3. Divide by the total number of data points (since it's a population standard deviation).
4. Take the square root of the result.

I'll calculate this next.### 2. Mean: The calculated mean number of hate crimes from 2007 to 2018 is approximately 6528.42.

3. Population Standard Deviation:

The population standard deviation is approximately 724.60.

Would you like further details on any of these calculations or the method used?

Here are 5 follow-up questions that you might find interesting:

1. How does the standard deviation help us understand the data spread?
2. What does the skewness of the data indicate about changes in hate crimes over time?
3. Could we fit a trend line to the data, and what type of model might fit best?
4. How could the median be helpful in this context compared to the mean?
5. How would you compare the standard deviation with the variance?

Tip: When interpreting a distribution, always look at both the skewness and the mean to get a clear picture of how data points are spread.