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The question you've uploaded appears to be discussing a statistical concept related to the sum of squared deviations from the mean, often referred to as the "sum of squared distances" or variance in some contexts. Here's a breakdown of the elements:

1. The formula at the top shows the sum of squared deviations:

   \[
   f_1 \left( x_1 - \bar{x} \right)^2 + \dots + f_n \left( x_n - \bar{x} \right)^2
   \]

   This seems to represent a weighted sum of squared distances, where \( f_1, f_2, \dots, f_n \) are possibly frequencies or weights, and \( \bar{x} \) is the mean.

2. The multiple-choice question following this involves:
   - Adding a new point to a study, which will either increase or decrease the sum of squared distances.
   - The choices include options related to the sum being "larger" or "smaller" after the addition.

### Answering the Question:
The new participant adds 7 minutes of deviation (the added value), which affects the sum of squared deviations. If the new value is far from the mean, the sum of squared deviations will increase. If the value is close to the mean, the sum will decrease.

So, if the new value (7 minutes) significantly differs from the current average, the most likely answer is:

- **Larger** (which corresponds to the first option in the multiple-choice list: גדול/גדולה).

Would you like a more detailed explanation of this concept or to discuss the calculation further?

### Additional Questions:
1. What is the precise role of \( f_1, f_2, \dots, f_n \) in this formula—are they frequencies?
2. How is the mean \( \bar{x} \) computed in this particular problem? 
3. What was the sample size before the addition of this new value?
4. What is the precise definition of variance in your study? Does it match with the general definition?
5. How are outliers treated in this dataset when calculating the sum of squared deviations?

### Tip:
When adding a new data point to a dataset, always consider how far that point is from the mean, as it has the most direct impact on the sum of squared deviations or variance.

הצטרף למחקר, שביצע את התשומה ב-7 דקות. לאחר הצטרפות הנתון, סכום ריבועי המרחקים ____

Explore how the sum of squared deviations changes when a new data point, 7 minutes from the mean, is added to the dataset. This statistical problem is suitable for Grades 10-12 and covers key concepts like variance and sum of squared deviations.

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