Question 1

Which of the following best describes an outlier in a data set?

Accepted Answer

A value that is far removed from the overall pattern of the data (an extreme value).

Question 2

Which measure of center is most resilient to outliers?

Accepted Answer

Sample median

Question 3

Given the data set: 10, 15, 20, 25, 30, what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = 20$$

Question 4

Which formula correctly calculates the sample variance $$s^2$$ using the shortcut method?

Accepted Answer

$$s^2$$ = \frac{\sum $$x^2$$ - (\sum $$x)^2/n$$}{n-1}$$

Question 5

A professional basketball player scored 2312 points in 79 games. What was their average points per game?

Accepted Answer

29.3 points per game

Question 6

Which of the following is NOT a measure of variation (spread) in a data set?

Accepted Answer

Sample median

Question 7

If a data set is normally distributed, what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

95%

Question 8

Which of the following is the correct formula for a z-score?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 9

A data set has a mean of 67.1 and a standard deviation of 10.3. According to the Empirical Rule, what is the approximate range that contains 68% of the data?

Accepted Answer

From 56.8 to 77.4

Question 10

Which of the following statements about the sample mean and standard deviation is TRUE?

Accepted Answer

The mean describes the center, but the standard deviation is needed to tell a more complete story about the data.

Question 11

If you remove an outlier from a data set, what is a potential risk according to the study materials?

Accepted Answer

It may be misleading and could qualify as self-interest bias and an abuse of statistics.

Question 12

Which measure of center is best used when the data set contains extreme values (outliers)?

Accepted Answer

Sample median

Question 13

What is the general rounding rule for computed statistics?

Accepted Answer

Round to one more decimal place than is present in the original data.

Question 14

Which of the following is NOT part of the sample five-number summary?

Accepted Answer

Mean

Question 15

According to Chebyshev's Rule, what is the minimum percentage of data that will fall within $$k = 2$$ standard deviations of the mean for any data set?

Accepted Answer

75%

Question 16

If a data set has a mean of 20 and a standard deviation of 0, what can you conclude about the data?

Accepted Answer

All values are equal to 20.

Question 17

Which of the following best describes the effect of increasing variation (spread) in a data set?

Accepted Answer

The standard deviation increases.

Question 18

A student scored 1.5 standard deviations above the mean on an exam. What is their z-score?

Accepted Answer

$$z = 1.5$$

Question 19

Which of the following is true about the sample range?

Accepted Answer

It is calculated as the difference between the largest and smallest values in the data set.

Question 20

If a data set is not normally distributed, which rule can still be used to estimate the minimum proportion of data within k standard deviations of the mean?

Accepted Answer

Chebyshev's Rule

Describing, Exploring, and Comparing Data: Measures of Center, Variation, and Relative Standing

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