Q: A data value is considered an outlier in a modified boxplot if it is:

More than $$1.5 \times IQR$$ above $$Q_3 or $$below $$Q_1$$

Question 1

Which of the following statements best describes why the mean is not considered a resistant measure of center?

Accepted Answer

The mean can change substantially if there is an extreme value (outlier) in the data set.

Question 2

Given the following data set representing the number of hours five students studied for an exam: 2, 4, 6, 8, 10. What is the median?

Accepted Answer

$$6$$

Question 3

A sample of five smartphone data speeds (in Mbps) is: 38.5, 55.6, 22.4, 14.1, 23.1. What is the midrange of this data set?

Accepted Answer

$$\frac{55.6 + 14.1}{2} = 34.85$$

Question 4

Which measure of center is most appropriate for describing the typical value of a highly skewed distribution, such as household income?

Accepted Answer

Median

Question 5

A frequency distribution has the following data: $$\sum f = 50$$ and $$\sum (f \cdot x) = 8025.0. $$What is the mean of the data set?

Accepted Answer

$$\frac{8025.0}{50} = 160.5$$

Question 6

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is a resistant measure of variation.

Question 7

A data set has a mean of $$100$$ and a standard deviation of $$15. $$According to the empirical rule, approximately what percentage of values fall between $$85$$ and $$115$$?

Accepted Answer

About $$68\%$$

Question 8

If a data value has a z score of $$-2.56$$, what can you conclude about this value?

Accepted Answer

It is significantly low.

Question 9

Given a sample with $$n = 5$$, $$\sum x = 153.7$$, and $$\sum x^2$ = 5807.79$$, what is the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{\frac{5 \cdot 5807.79 - (153.7)^2$}{5 \cdot 4}} = 16.45$$

Question 10

A student’s grades and course credits are: A (3 credits), A (4 credits), B (3 credits), C (3 credits), F (1 credit). Using the quality points A=4, B=3, C=2, F=0, what is her GPA?

Accepted Answer

$$\frac{3 \cdot 4 + 4 \cdot 4 + 3 \cdot 3 + 3 \cdot 2 + 1 \cdot 0}{3 + 4 + 3 + 3 + 1} = 3.07$$

Question 11

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 12

A boxplot is constructed using which of the following values?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 13

If a data set has a mean of $$50$$ and a standard deviation of $$5$$, what is the z score for a value of $$60$$?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 14

Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} \cdot 100$$

Question 15

A data set has a minimum value of $$2$$, a first quartile $$Q_1 = 5$, a median of 8$, a third quartile Q_3$ = 12$$, and a maximum value of $$20. $$Which value is the interquartile range?

Accepted Answer

$$12 - 5 = 7$$

Question 16

Which of the following is true about Chebyshev’s Theorem?

Accepted Answer

It applies to any data set, regardless of shape.

Question 17

A data value is considered an outlier in a modified boxplot if it is:

Accepted Answer

More than $$1.5 	imes IQR$$ above $$Q_3 or $$below $$Q_1$$

Question 18

Which of the following is a correct interpretation of a percentile?

Accepted Answer

The 40th percentile is the value below which 40% of the data fall.

Chapter 3: Describing, Exploring, and Comparing Data – Study Notes

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