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 IQR$$ or less than Q_1$ - 1.5 \times IQR is $$considered an outlier.

Question 1

Which of the following best describes the 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 a class, while class boundaries are the numbers that separate classes without forming gaps between them.

Question 2

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

Accepted Answer

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

Question 3

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

$$4$$

Question 4

A data set has a mean of $$5.2$$, a median of $$5$$, and a mode of $$4. $$Which of the following is true about the mode in this context?

Accepted Answer

The mode does not represent the center because it is the smallest data value.

Question 5

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

Accepted Answer

It can only be used if the data distribution is approximately symmetric and bell-shaped.

Question 6

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 7

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 IQR$$ or less than Q_1$ - 1.5 	imes IQR is $$considered an outlier.

Question 8

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

Accepted Answer

One quarter (25%) of the data set.

Question 9

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

Accepted Answer

To make it easier to detect patterns in the data.

Question 10

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

Accepted Answer

$$1$$

Question 11

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

Accepted Answer

Class width is the distance between the lower (or upper) limits of consecutive classes.

Question 12

A graph of cumulative frequencies (ogive) always:

Accepted Answer

Increases from left to right.

Question 13

Which measure of central tendency is most likely to be affected by an outlier?

Accepted Answer

Mean

Question 14

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? (A=4, B=3, C=2, D=1)

Accepted Answer

$$2.4$$

Question 15

Given the following frequency distribution for gas mileage (in miles per gallon) for 31 cars:

26-29: 10
30-33: 13
34-37: 2
38-41: 6

What is the approximate mean of the frequency distribution?

Accepted Answer

$$32.0$$

Question 16

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 higher standard deviation means more values are further from the mean.

Question 17

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

Accepted Answer

The student's grade is below the average.

Question 18

Suppose you have a data set: $$1, 3, 3, 4, 5, 5. $$Which of the following is true?

Accepted Answer

The data set is bimodal and the mean and median are the same.

Question 19

Which of the following best describes relative frequency?

Accepted Answer

The percentage of the data that falls in a given class.

Question 20

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

Accepted Answer

The distribution is symmetric.

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