https://file.aiquickdraw.com/mathbot/file/17254639519313zxdjzx9.jpg

The image contains two questions:

**Question 1:**
It asks about the mean of the data points shown in Figure 1, assuming that the data points lie on the locus of the curve shown. The figure depicts an ellipse centered at the origin (0,0) on the graph with x1 and x2 axes. The options provided are:
- (4,4)
- (0,0)
- (5,3)
- (3,5)

Since the ellipse is centered at the intersection of the x1 and x2 axes, the mean of the data points should be at the center of the ellipse, which is (0,0). 

**Answer:** (0,0)

**Question 2:**
It is a multiple-choice question related to MDA (likely referring to Mean Deviation Analysis or Multivariate Discriminant Analysis), asking which of the following statements are true:
- I. Maximize the inter-class variance
- II. Maximize the intra-class variance
- III. Minimize the intra-class variance

Options:
- Only I
- Only I and III
- Only II
- All I, II, and III

The correct approach in most MDA-related problems involves maximizing the inter-class variance (distinguishing between classes) and minimizing the intra-class variance (tightening the data within each class). Thus, statements I and III are correct.

**Answer:** Only I and III

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Would you like a more detailed explanation of these questions, or do you have any other questions?

### Related Questions:
1. What is the formula for the mean of data points?
2. How do you find the center of an ellipse?
3. What is the role of inter-class variance in data analysis?
4. Why is intra-class variance minimized in MDA?
5. How is an ellipse represented mathematically?

**Tip:** In data analysis, always identify the key attributes (mean, variance) that

Assuming the data points lie on the locus of the curve shown in Figure 1 and each of the horizontal and vertical lines are 1 unit apart from each other, which of the following points best describes the mean of the data points? (0,0) is the intersection point of the X1 and Y axes.
Which of the following is true for MDA?
I. Maximize the inter-class variance
II. Maximize the intra-class variance
III. Minimize the intra-class variance.

This problem involves finding the mean of data points on an ellipse centered at the origin and understanding the concepts of inter-class and intra-class variance in Multivariate Discriminant Analysis (MDA). Perfect for students in Grades 11-12.

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