To calculate the squared deviations of a dataset, we follow these steps:

1. Find the Mean (Average):
   $\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$

2. Calculate the Deviations:
   Subtract the mean from each data point.

3. Square the Deviations:
   Square each of the deviations calculated in step 2.

Let's go through these steps:

1. Calculate the Mean

$\text{Mean} = \frac{5 + (-12) + 5 + (-12) + 5 + (-12) + (-7)}{7} = \frac{-28}{7} = -4$

2. Calculate the Deviations

• For 5: $5 - (-4) = 9$
• For -12: $-12 - (-4) = -8$
• For 5: $5 - (-4) = 9$
• For -12: $-12 - (-4) = -8$
• For 5: $5 - (-4) = 9$
• For -12: $-12 - (-4) = -8$
• For -7: $-7 - (-4) = -3$

3. Square the Deviations

• $9^2 = 81$
• $(-8)^2 = 64$
• $9^2 = 81$
• $(-8)^2 = 64$
• $9^2 = 81$
• $(-8)^2 = 64$
• $(-3)^2 = 9$

Squared Deviations:

• 81, 64, 81, 64, 81, 64, 9

Would you like any more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you calculate the variance of this dataset using squared deviations?
2. What is the standard deviation of this dataset?
3. How would the squared deviations change if all values in the dataset were increased by 3?
4. How do squared deviations relate to the concept of "sum of squares" in statistics?
5. What are some real-world applications of calculating squared deviations?

Tip: Squared deviations are always non-negative, which is why they are often used in statistical measures like variance to avoid the canceling out of positive and negative deviations.