The image displays formulas for Mean and Variance. There is no specific question asked.

Here are the formulas for Mean and Variance as shown in the image:

MEAN

• Sample Mean: $$\bar{x} = \frac{\sum x}{n}$$
• Population Mean: $$\mu = \frac{\sum x}{N}$$
• Mean for grouped data (or weighted mean): $$\bar{x} = \mu = \frac{\sum fx}{\sum f}$$

VARIANCE

• Sample Variance (computational formula): $$S^2 = \frac{1}{n-1} \left(\sum x^2 - \frac{(\sum x)^2}{n}\right)$$
• Sample Variance (definition formula): $$S^2 = \frac{\sum (x-\bar{x})^2}{n-1}$$
• Sample Variance for grouped data: $$S^2 = \frac{\sum f(x-\bar{x})^2}{n-1}$$
• Population Variance (definition formula): $$\sigma^2 = \frac{\sum (x-\mu)^2}{N}$$
• Population Variance for grouped data: $$\sigma^2 = \frac{\sum f(x-\mu)^2}{N}$$
• Population Variance (computational formula): $$\sigma^2 = \frac{1}{N} \left(\sum x^2 - \frac{(\sum x)^2}{N}\right)$$

Relationship between n, N, and $\sum f$

• $n = N = \sum f$