To compute the summation, $\sum (X - \bar{X})^2$, the values provided in the input need to be summed directly. Let’s compute the total step by step:

Input Values:

• $4786.38$
• $3498.38$
• $2414.58$
• $849.58$ (repeated thrice, so add three times)
• $366.58$
• $17.14$
• $0.74$ (repeated thrice, so add three times)
• $14.82$
• $34.43$
• $117.98$ (repeated six times, so add six times)
• $251.68$ (repeated twice, so add twice)
• $318.58$
• $394.66$
• $435.70$ (repeated ten times, so add ten times)

Calculation:

We will add all the numbers together, accounting for repetitions. Let me compute this. Define the values and their repetitions values = { 4786.38: 1, 3498.38: 1, 2414.58: 1, 849.58: 3, 366.58: 1, 17.14: 1, 0.74: 3, 14.82: 1, 34.43: 1, 117.98: 6, 251.68: 2, 318.58: 1, 394.66: 1, 435.70: 10 }

Calculate the total summation

summation = sum(value * count for value, count in values.items()) summationThe summation $\sum (X - \bar{X})^2$ is $19,964.75$.

Would you like a breakdown of the steps or additional help?

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5 Related Questions:

1. What is the significance of $\sum (X - \bar{X})^2$ in statistics?
2. How does $\sum (X - \bar{X})^2$ relate to variance and standard deviation?
3. Can you verify the mean $\bar{X}$ of this dataset and calculate variance?
4. How would adding more data points affect the summation?
5. What are practical examples of using $\sum (X - \bar{X})^2$ in real-world applications?

Tip:

To calculate variance, divide $\sum (X - \bar{X})^2$ by the total number of data points (or $n-1$ for a sample).