Q: Given a dataset with $$Q_1 = 23$, Q_3$ = 36.5$$, and $$IQR = Q_3$ - Q_1$, what is the lower limit for identifying potential outliers?

$$Q_1 - 1.5$$ \times IQR = 23 - 1.5 \times 13.5 = 2.75$$

Q: If $$Q_1 = 23$, Q_3$ = 36.5$$, and $$IQR = 13.5$$, what is the upper limit for identifying potential outliers?

$$Q_3 + 1.5$$ \times IQR = 36.5 + 1.5 \times 13.5 = 56.75$$

Question 1

Which of the following is NOT included in the five-number summary of a dataset?

Accepted Answer

The mean

Question 2

Given a dataset with $$Q_1 = 23$, Q_3$ = 36.5$$, and $$IQR = Q_3$ - Q_1$, what is the lower limit for identifying potential outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 23 - 1.5 	imes 13.5 = 2.75$$

Question 3

A boxplot of GDP per capita for continents in 2007 shows several dots outside the whiskers for Africa. What do these dots represent?

Accepted Answer

Potential outliers

Question 4

Which measure of center is considered resistant to extreme values?

Accepted Answer

The median

Question 5

If a boxplot has a longer right whisker and the median is closer to the left of the box, how is the data distributed?

Accepted Answer

Right-skewed

Question 6

Given the weekly TV-viewing hours: 5, 15, 16, 20, 21, 25, 26, 27, 30, 30, 31, 32, 32, 34, 35, 38, 38, 41, 43, 66, what is the median ($$Q_2$$)?

Accepted Answer

32

Question 7

Which formula correctly calculates the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 8

A dataset has $$\bar{x} = 50$$ and $$s = 7.4. $$According to the three-standard-deviations rule, almost all observations should lie within which interval?

Accepted Answer

$$[\bar{x} - 3s, \bar{x} + 3s] = [50 - 22.2, 50 + 22.2] = [27.8, 72.2]$$

Question 9

If the number of observations in a dataset is odd, how is the median included when splitting the data for quartile calculation?

Accepted Answer

Include the median in both halves

Question 10

Which of the following best describes adjacent values in a boxplot?

Accepted Answer

The most extreme observations that lie within the lower and upper limits

Question 11

A boxplot for GDP per capita in Europe shows a symmetric box and whiskers. What does this indicate about the distribution?

Accepted Answer

The distribution is approximately symmetric

Question 12

Which of the following is a resistant measure of spread?

Accepted Answer

Interquartile range (IQR)

Question 13

If $$Q_1 = 23$, Q_3$ = 36.5$$, and $$IQR = 13.5$$, what is the upper limit for identifying potential outliers?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 36.5 + 1.5 	imes 13.5 = 56.75$$

Question 14

Which scenario would most likely result in a left-skewed boxplot?

Accepted Answer

A dataset with a few extremely low values

Question 15

Why is the median considered a resistant measure?

Accepted Answer

It is not affected by extreme values

Question 16

In the context of income distribution across continents, which measure would best summarize the typical income while minimizing the effect of outliers?

Accepted Answer

The median

Question 17

A dataset has $$Q_1 = 10$, Q_2$ = 20$$, $$Q_3 = 30$, and a maximum value of 100. Which value is most likely an outlier?

Accepted Answer

100

Question 18

Which of the following statements about boxplots is TRUE?

Accepted Answer

Boxplots display the five-number summary and highlight potential outliers

Question 19

If a dataset's boxplot has a longer left whisker and the median is closer to the right of the box, what does this indicate?

Accepted Answer

The data is left-skewed

Question 20

Which of the following is the correct order for the five-number summary?

Accepted Answer

Minimum, $$Q_1$$, Median ($$Q_2$$), $$Q_3$$, Maximum

Descriptive Measures: Five-Number Summary, Boxplot, and Data Variation

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