The table below sows the number of hate crimes for 2007 to 2018. The value for 2007 is slightly different than the actual value so that each student gets their own unique problem.

Year

Number of hate crimes

2007

7635

2008

7783

2009

6604

2010

6628

2011

6222

2012

5796

2013

5928

2014

5479

2015

5850

2016

6121

2017

7175

2018

7120

Here is the data so you can copy and paste special it into the raw data sheet.

Number of hate crimes

7635

7783

6604

6628

6222

5796

5928

5479

5850

6121

7175

7120

1. You can see the graph of the actual data points at this site here. What type of distribution do you think this is?

Normal distribution

Skewed right

Skewed left

Flat distribution

2. What is the mean?

3. What is the population standard deviation?

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.

The table below shows the number of hate crimes for 2007 to 2018. The value for 2007 is slightly different than the actual value so that each student gets their own unique problem.

Year
Number of hate crimes
2007: 7635
2008: 7783
2009: 6604
2010: 6628
2011: 6222
2012: 5796
2013: 5928
2014: 5479
2015: 5850
2016: 6121
2017: 7175
2018: 7120

What type of distribution do you think this is?
- Normal distribution
- Skewed right
- Skewed left
- Flat distribution

What is the mean?
What is the population standard deviation?

Analyze hate crime data from 2007 to 2018 by calculating the mean and population standard deviation. Explore the distribution pattern (skewed left) and learn key statistical concepts, including central tendency and dispersion. Suitable for students in Grades 10-12.

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