Q: What is the median of the sample: 2, 10, 30, 35, 38, 42, 50, 60, 62, 110?

$$\text{Median} = \frac{38 + 42}{2} = 40$$

Q: For the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110, what is the lower fence for detecting outliers?

$$\text{Lower Fence} = Q_1$ - 1.5 \times IQR = 30 - 1.5 \times 30 = -15$$

Question 1

Given the sample: 2, 10, 30, 35, 38, 42, 50, 60, 62, 110, what is the interquartile range (IQR) for this data set?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 60 - 30 = 30$$

Question 2

Which value in the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110 is considered an outlier according to the 1.5*IQR rule?

Accepted Answer

110

Question 3

What is the median of the sample: 2, 10, 30, 35, 38, 42, 50, 60, 62, 110?

Accepted Answer

$$	ext{Median} = \frac{38 + 42}{2} = 40$$

Question 4

For the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110, what is the lower fence for detecting outliers?

Accepted Answer

$$	ext{Lower Fence} = Q_1$ - 1.5 	imes IQR = 30 - 1.5 	imes 30 = -15$$

Question 5

A boxplot is constructed for the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110. Which of the following statements is true?

Accepted Answer

The value 110 will be plotted as an outlier, shown as a dot beyond the upper whisker.

Question 6

Given the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110, what is the value of $$Q_1 ($$the first quartile)?

Accepted Answer

$$Q_1 = 30$

Question 7

For the same sample, what is the value of $$Q_3 ($$the third quartile)?

Accepted Answer

$$Q_3 = 60$

Question 8

Which of the following best describes the skewness of the sample 2, 10, 30, 35, 38, 42, 50, 60, 62, 110?

Accepted Answer

Positively skewed (right-skewed)

Question 9

If you were to add the value 200 to the sample, how would this affect the boxplot?

Accepted Answer

The value 200 would be plotted as an additional outlier, further increasing the upper range.

Question 10

Which of the following is NOT a correct interpretation of a boxplot?

Accepted Answer

The whiskers always extend to the minimum and maximum values, regardless of outliers.

Question 11

Suppose you have a boxplot with a long upper whisker and several outliers above the box. What does this indicate about the data?

Accepted Answer

The data is positively skewed with high-value outliers.

Question 12

If the median is closer to the lower quartile ($$Q_1) $$than the upper quartile ($$Q_3) in a $$boxplot, what does this suggest about the distribution?

Accepted Answer

The distribution is positively skewed.

Constructing a Boxplot from a Sample

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