Q: How can the interquartile range (IQR) be used to identify outliers in a data set?

Any data value greater than $$Q_3 + 1.5$$ \times \text{IQR}$$ or less than Q_1$ - 1.5 \times \text{IQR} is $$considered an outlier.

Question 1

Which of the following best describes the benefit of using a frequency distribution to represent a data set?

Accepted Answer

It allows for easier identification of patterns within the data.

Question 2

What is the main difference between class limits and class boundaries in a frequency distribution?

Accepted Answer

Class limits are the least and greatest numbers that can belong to the class, while class boundaries are the numbers that separate classes without forming gaps.

Question 3

A frequency polygon and an ogive are both graphical representations of frequency distributions. Which statement correctly distinguishes them?

Accepted Answer

A frequency polygon displays class frequencies, while an ogive displays cumulative frequencies.

Question 4

Given the following frequency distribution for temperatures (in degrees F):
35-39: 1
40-44: 3
45-49: 5
50-54: 11
55-59: 7
60-64: 7
65-69: 1
What is the class width?

Accepted Answer

The class width is $$5.$$

Question 5

A data set has a mean of $$5.2$$, a median of $$5$$, and a mode of $$4. $$Which measure of central tendency is most likely to be affected by an outlier?

Accepted Answer

The mean

Question 6

Which of the following statements about the Empirical Rule is correct?

Accepted Answer

The Empirical Rule can only be used if the distribution is approximately symmetric and bell-shaped.

Question 7

A guest lecturer's talk represents the third quartile ($$Q_3) $$for talks in a lecture series. What does this indicate about the length of the talk?

Accepted Answer

The talk is longer than 75% of the lectures in the series.

Question 8

How can the interquartile range (IQR) be used to identify outliers in a data set?

Accepted Answer

Any data value greater than $$Q_3 + 1.5$$ 	imes 	ext{IQR}$$ or less than Q_1$ - 1.5 	imes 	ext{IQR} is $$considered an outlier.

Question 9

On a box-and-whisker plot, what proportion of the data set lies on the left whisker?

Accepted Answer

One quarter

Question 10

Why should the number of classes in a frequency distribution be between 5 and 20?

Accepted Answer

To make it easier to detect patterns in the data.

Question 11

After constructing a frequency distribution, what should the sum of the relative frequencies be?

Accepted Answer

The sum should be $$1.$$

Question 12

Which of the following statements about cumulative frequency graphs (ogives) is correct?

Accepted Answer

The graph always increases from left to right.

Question 13

A student receives the following grades: B in two 2-credit classes, D in one 4-credit class, A in one 3-credit class, and C in one 3-credit class. What is the student's weighted mean grade point score?

Accepted Answer

The weighted mean is $$2.4$$

Question 14

You are applying for a job at two companies. Company A offers starting salaries with $$\mu = 25,000$$ and $$\sigma = 1,000. $$Company B offers starting salaries with $$\mu = 25,000$$ and $$\sigma = 3,000. $$From which company are you more likely to get an offer of $$27,000 or $$more?

Accepted Answer

Company B, because a larger standard deviation means more values are farther from the mean.

Question 15

A student's grade on the Fundamentals of Engineering exam has a $$z-$$score of $$-0.5. $$What does this indicate?

Accepted Answer

The student's grade was below the average.

Question 16

Given the data set: $$64, 60, 57, 57, 57, 64, 61, 62, 58, 54, 60, 61, 57, 63, 78$$, what is the interquartile range (IQR)?

Accepted Answer

The IQR is $$6$$

Question 17

If a frequency distribution has each class with the same frequency, what can be said about the distribution?

Accepted Answer

The distribution is symmetric.

Question 18

Which of the following is the correct formula for the midpoint of a class interval from $$a to$$ $$b$$?

Accepted Answer

Midpoint $$= \frac{a + b}{2}$$

Question 19

Which of the following statements about class width in a frequency distribution is correct?

Accepted Answer

Class width is the distance between the lower limits of consecutive classes.

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