Q: A dataset has $$Q_1 = 20$, Q_3$ = 40. $$What is the upper fence for outliers using the 1.5×IQR rule?

$$40 + 1.5 \times (40 - 20) = 70$$

Question 1

A city planner is analyzing the commuting times (in minutes) for 12 workers: 10, 12, 12, 15, 16, 17, 18, 18, 20, 22, 22, 90. Which measure of center would be most affected by the outlier, and why?

Accepted Answer

The mean, because it is calculated using all values and is pulled by the outlier.

Question 2

Given the dataset: 5, 7, 8, 10, 12, 13, 15, 18, 20, 25, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 18 - 8 = 10$$

Question 3

Which of the following best describes a right-skewed distribution?

Accepted Answer

The mean is greater than the median.

Question 4

A researcher collects the following data: 2, 4, 4, 5, 7, 8, 9. What is the mode of this dataset?

Accepted Answer

4

Question 5

Which formula correctly calculates the sample standard deviation for a dataset $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\overline{x}$$?

Accepted Answer

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

Question 6

A dataset has a mean of 50 and a standard deviation of 5. According to the empirical rule, about 95% of the data falls within what interval?

Accepted Answer

$$[40, 60]$$

Question 7

Which summary statistic is most appropriate for describing the center of a highly skewed distribution?

Accepted Answer

Median

Question 8

A boxplot shows a long right whisker. What does this indicate about the distribution?

Accepted Answer

The distribution is right-skewed.

Question 9

Which rule would you use to identify outliers in a dataset using quartiles?

Accepted Answer

1.5×IQR Rule

Question 10

A company’s delivery times have a mean of 3.5 days and a standard deviation of 1.5 days. Another company has a mean of 3.5 days and a standard deviation of 4 days. What does this suggest about the two companies?

Accepted Answer

The first company’s delivery times are more consistent.

Question 11

Which of the following is NOT a component of the five-number summary?

Accepted Answer

The mean

Question 12

If a dataset is approximately symmetric and has no outliers, which measure of center and spread should you report?

Accepted Answer

Mean and standard deviation

Question 13

A student calculates the z-score for a value as $$z = 2.5. $$What does this indicate?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 14

Which of the following best describes the effect of squaring deviations when calculating variance?

Accepted Answer

It makes all deviations positive and gives more weight to larger deviations.

Question 15

A dataset has $$Q_1 = 20$, Q_3$ = 40. $$What is the upper fence for outliers using the 1.5×IQR rule?

Accepted Answer

$$40 + 1.5 	imes (40 - 20) = 70$$

Question 16

Which summary statistic is most appropriate for ordinal data, such as Likert scale responses?

Accepted Answer

Median

Question 17

If a distribution is left-skewed, which of the following is true?

Accepted Answer

The mean is less than the median.

Question 18

Why is the IQR considered a resistant measure of spread?

Accepted Answer

It is not affected by extreme values or outliers.

Question 19

A dataset has the following five-number summary: min = 12, $$Q_1 = 18$, median = 22, Q_3$ = 30$$, max = 90. Which value is most likely an outlier?

Accepted Answer

90

Describing Data with Numbers: Measures of Center, Variability, Outliers, and Summary Statistics

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