Q: If the interquartile range (IQR) for a data set is $$0.9$$, what are the lower and upper fences for outliers if $$Q_1 = 6.7$ and Q_3$ = 7.6$$?

Lower fence: $$6.7 - 1.5 \times 0.9 = 5.35$$, Upper fence: $$7.6 + 1.5 \times 0.9 = 8.95$$

Question 1

Which measure of center is more resistant to outliers in a data set, and why?

Accepted Answer

The median, because it is not affected by extreme values.

Question 2

A data set of flight cancellations has one month with a cancellation rate of 20%, while most months are below 5%. What effect does this outlier have on the mean and median?

Accepted Answer

The mean increases more than the median.

Question 3

Given the following data set: $$10, 20, 30, 40, 50, 60$$, calculate the mean $$\bar{x}.$$

Accepted Answer

$$\bar{x} = \frac{10 + 20 + 30 + 40 + 50 + 60}{6} = 35$$

Question 4

Which of the following best describes the standard deviation?

Accepted Answer

The average distance from the mean, in the original units.

Question 5

For the data set $$10, 10, 10, 60, 60, 60$$, what is the mean and standard deviation?

Accepted Answer

Mean = $$35$$, Standard deviation = $$27.4$$

Question 6

Which rental fleet has a larger standard deviation in miles per gallon: Fleet #1 ($$10, 20, 30, 40, 50, 60) or $$Fleet #2 ($$10, 10, 10, 60, 60, 60$$)?

Accepted Answer

Fleet #2, because its values are more concentrated at the extremes.

Question 7

What is the formula for the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 8

A boxplot displays which of the following?

Accepted Answer

The 5-number summary and outliers.

Question 9

If the interquartile range (IQR) for a data set is $$0.9$$, what are the lower and upper fences for outliers if $$Q_1 = 6.7$ and Q_3$ = 7.6$$?

Accepted Answer

Lower fence: $$6.7 - 1.5 	imes 0.9 = 5.35$$, Upper fence: $$7.6 + 1.5 	imes 0.9 = 8.95$$

Question 10

Which of the following is NOT part of the five-number summary?

Accepted Answer

The mean

Question 11

A data set is highly skewed to the right. Which measure of center is most appropriate to report?

Accepted Answer

The median, because it is less affected by skewness.

Question 12

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

Accepted Answer

The difference between the third and first quartiles: $$IQR = Q_3$ - Q_1$

Question 13

If a boxplot shows several points beyond the upper fence, what does this indicate?

Accepted Answer

There are multiple outliers above the third quartile.

Question 14

Which of the following is the correct formula for the lower fence in a boxplot?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR$$

Question 15

A researcher uses StatCrunch to summarize a column of data. Which menu path should they follow to find the quartiles?

Accepted Answer

Stat \u003e Summary Stats \u003e Columns

Question 16

Why is the standard deviation not a resistant measure of spread?

Accepted Answer

Because it is affected by extreme values and outliers.

Question 17

If the median of a data set is 3.4, the first quartile is 2.2, and the third quartile is 4.35, what is the interquartile range?

Accepted Answer

$$IQR = 4.35 - 2.2 = 2.15$$

Question 18

Which of the following statements about percentiles is correct?

Accepted Answer

The 25th percentile is the first quartile ($$Q_1).$$

Describing Data Numerically: Mean, Median, Standard Deviation, and Boxplots

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