calculate the sum of (x-mean)^2 of the following rainfall millimeters: 658,864,891,916,1259,976,809,950,1135,854,839,837,771,1229,786,652,750,708,953,746,802,1011,800,1150,734,715,789,1307,750

To calculate the sum of \((x - \text{mean})^2\) for the given rainfall data, we need to follow these steps:

1. **Find the mean of the rainfall values.**
2. **Subtract the mean from each value (\(x - \text{mean}\)).**
3. **Square the result of each difference.**
4. **Sum the squared differences.**

Let's go through the process:

### Step 1: Find the Mean
The given rainfall values are:
\[ 658, 864, 891, 916, 1259, 976, 809, 950, 1135, 854, 839, 837, 771, 1229, 786, 652, 750, 708, 953, 746, 802, 1011, 800, 1150, 734, 715, 789, 1307, 750 \]

First, find the sum of all the values and then divide by the total number of values (28):

\[
\text{Mean} = \frac{\text{Sum of values}}{n}
\]

Let me calculate that now. numpy as np

# Given rainfall values
rainfall_values = [658, 864, 891, 916, 1259, 976, 809, 950, 1135, 854, 839, 837, 771, 1229, 786, 652, 750, 708, 953, 746, 802, 1011, 800, 1150, 734, 715, 789, 1307, 750]

# Calculate the mean
mean_rainfall = np.mean(rainfall_values)
mean_rainfallThe mean of the rainfall values is approximately \( 884.17 \) millimeters.

### Step 2: Subtract the Mean from Each Value
We will now subtract the mean from each rainfall value.

### Step 3: Square the Differences
Next, we square the differences obtained in the previous step.

### Step 4: Sum the Squared Differences
Finally, we will sum all the squared differences to get the required value.

Let me calculate that now. Calculate the squared differences (x - mean)^2
squared_differences = [(x - mean_rainfall)**2 for x in rainfall_values]

# Sum of squared differences
sum_squared_differences = sum(squared_differences)
sum_squared_differencesThe sum of the squared differences, \((x - \text{mean})^2\), for the given rainfall data is approximately \( 905,348.14 \) millimeters squared.

If you'd like more details or have any questions, feel free to ask! Here are some related questions:

1. How do you calculate the variance from the sum of squared differences?
2. How can you use the standard deviation to interpret this data?
3. What does a large sum of squared differences indicate about the dataset?
4. How would you calculate the standard deviation for this data?
5. What are some ways to visualize the spread of this data?

**Tip**: The sum of squared differences is closely related to the variance, and dividing it by the number of data points (or \(n-1\) for a sample) gives you the variance.

Learn how to calculate the sum of squared differences for rainfall data. In this problem, we calculate (x - mean)² for rainfall values such as 658, 864, 891, and more, ultimately summing the squared differences to obtain a result of approximately 905,348.14. Suitable for students in Grades 9-12 studying statistics.

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