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C3_W2_Practice-Quiz.md

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1.

$$\begin{matrix} \hline \text{Set} & | & \text{Values} \cr \hline 1 & | & 1 & 5 & 7 & 9 \cr 2 & | & -20 & -10 & 0 & 10 \cr 3 & | & 100 & 101 & 102 & 103 \cr 4 & | & -10 & -5 & 0 & -5 \cr \hline \end{matrix}$$

Consider the four sets of samples above. Which one has the smallest variance?

  • $1$
  • $2$
  • $3$
  • $4$

2. About the mean, mode and median, it is correct to say (check all that apply).

  • The mean is always greater than or equal to the median.
  • The median is more stable to outliers than the mean.
  • The mode is the most frequent value in a sample.
  • There can be more than one mode ins a sample.

3. Consider the following independent random variables:

$$X \thicksim \text{Normal} \left( 3, 1^{2} \right)$$ $$Y \thicksim \text{Normal} \left( 2, 2^{2} \right)$$

Then $Z = X + Y \thicksim \text{Normal} \left( \mu, \sigma^{2} \right)$, where $\mu$, $\sigma$ are equal to:

  • $\mu = \sqrt{5}, \sigma = \sqrt{3}$
  • $\mu = 5, \sigma = \sqrt{5}$
  • $\mu = 5, \sigma = \sqrt{3}$
  • $\mu = 5, \sigma = 5$

4. What is the advantage of looking at the standard deviation instead of the variance?

  • The standard deviation is less affected by outliers than the variance.
  • The standard deviation has the same dimension as the sample.
  • The standard deviation may be negative.
  • There are no advantages. They mean the same thing.

5. Which of the following best describes the purpose of a QQ plot?

  • To visualize the distribution of a dataset
  • To visualize the relationship between two datasets
  • To test for normality of a dataset
  • To test for independence between two datasets

6. Which of the following is true about a box plot with a long whisker on the upper end?

  • The data is negatively skewed
  • The data is positively skewed
  • The data is normally distributed
  • There are no outliers

7. Which of the following is a correct statement regarding a QQ plot?

  • If the points fall close to the diagonal, the data is not normally distributed
  • If the points fall close to the diagonal line, the data is normally distributed
  • If the points fall far from the diagonal line, the data is normally distributed
  • If the points fall far from the diagonal line, the data is not normally distributed

8. Consider the following box plot for the test scores of two classes, A and B:

missing

Which of the following statements is true?

  • The median score of Class A is higher than the median score of Class B.
  • The median score of Class B is higher than the median score of Class A.
  • The interquartile range of Class A is larger than the interquartile range of Class B.
  • The interquartile range of Class B is larger than the interquartile range of Class A.

9. Consider the following QQ plot for a set of data:

missing

Which of the following statements is true?

  • The data looks normally distributed.
  • The data is not normally distributed.
  • The data has a higher variance than a normal distribution.
  • The data has a lower variance than a normal distribution.