If the variance of a dataset is 50 and all data points are increased by 100% then what will be the variance?
O 50
Ο 100
○ 200
Ο 25

When all data points in a dataset are increased by 100%, it means each data point is multiplied by 2. 

Variance is affected by the square of the scaling factor applied to the data points. If each data point is multiplied by a constant \( k \), the variance is multiplied by \( k^2 \).

In this case, since each data point is multiplied by 2, the new variance will be:

\[
\text{New Variance} = k^2 \times \text{Original Variance} = 2^2 \times 50 = 4 \times 50 = 200
\]

So, the correct answer is:

○ 200

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:
1. How does adding a constant to each data point in a dataset affect the variance?
2. What is the relationship between standard deviation and variance?
3. If the standard deviation of a dataset is known, how do you calculate the variance?
4. What happens to the variance if each data point is divided by a constant?
5. How does variance differ from standard deviation in terms of interpretation?
6. What is the effect of multiplying all data points by a negative constant on the variance?
7. Can variance ever be negative? Why or why not?
8. How would you calculate the variance if you only have the mean and data points?

**Tip:** Remember, variance measures the spread of data points around the mean, and it's always non-negative.

Explore how scaling data points affect variance with an example calculation. Understand the impact of increasing all data points in a dataset by 100% on variance. Learn the variance formula application and its relevance in statistical analysis.

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