Q: Given the following ages of 25 patients: 42, 44, 44, 47, 50, 51, 52, 55, 55, 57, 58, 58, 60, 61, 61, 64, 68, 69, 71, 72, 80, 82, 85, what is the relative frequency of the bin 50 to 60?

$$\frac{9}{25} \times 100\% = 36\%$$

Q: What is the formula for the range of a dataset?

$$\text{Range} = \text{maximum} - \text{minimum}$$

Q: How are suspected outliers identified in a boxplot?

Observations above $$Q_3 + 1.5$$ \times \text{IQR}$$ or below Q_1$ - 1.5 \times \text{IQR}$$

Question 1

Which of the following best describes the left end-point convention when constructing frequency distributions?

Accepted Answer

All intervals (except the last one) include the left end-point but not the right.

Question 2

Given the following ages of 25 patients: 42, 44, 44, 47, 50, 51, 52, 55, 55, 57, 58, 58, 60, 61, 61, 64, 68, 69, 71, 72, 80, 82, 85, what is the relative frequency of the bin 50 to 60?

Accepted Answer

$$\frac{9}{25} 	imes 100\% = 36\%$$

Question 3

When constructing a histogram for quantitative data, what is plotted along the vertical axis?

Accepted Answer

The frequency or relative frequency

Question 4

In a stem-and-leaf display, what does the 'stem' represent for the value 137?

Accepted Answer

The digits 13

Question 5

Which of the following distributions is described as having one peak?

Accepted Answer

Unimodal

Question 6

A histogram shows a long tail to the right. How would you describe the shape of this distribution?

Accepted Answer

Skewed to the right

Question 7

Which measure of center is most appropriate for a distribution with significant outliers?

Accepted Answer

Median

Question 8

Given a dataset with $$n$$ observations, what is the formula for the mean?

Accepted Answer

$$\bar{y} = \frac{y_1$ + y_2$ + \ldots + y_n}{n}$$

Question 9

If a dataset has 26 observations, what is the location of the median?

Accepted Answer

The average of the 13th and 14th observations

Question 10

What is the formula for the range of a dataset?

Accepted Answer

$$	ext{Range} = 	ext{maximum} - 	ext{minimum}$$

Question 11

The interquartile range (IQR) is defined as:

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$

Question 12

Which of the following is TRUE about the standard deviation (SD)?

Accepted Answer

SD has the same unit as the observations.

Question 13

What is the formula for the sample variance $$s^2$$ for $$n$$ observations $$y_1$$, $$y_2$$, ..., y_n$$ with mean $$\bar{y}$$?

Accepted Answer

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

Question 14

Which summary statistic is NOT sensitive to outliers?

Accepted Answer

Interquartile Range (IQR)

Question 15

A boxplot is constructed using which summary statistics?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 16

How are suspected outliers identified in a boxplot?

Accepted Answer

Observations above $$Q_3 + 1.5$$ 	imes 	ext{IQR}$$ or below Q_1$ - 1.5 	imes 	ext{IQR}$$

Question 17

If a distribution is highly skewed, which pair of summary statistics should be reported?

Accepted Answer

Median and IQR

Question 18

Why do we use squared deviations when calculating variance?

Accepted Answer

To ensure all deviations are positive and to penalize larger deviations more.

Question 19

When comparing two distributions using histograms, what is important to ensure a fair comparison?

Accepted Answer

Use the same scale for both histograms.

Question 20

A dataset has the following five-number summary: minimum = 10, $$Q_1 = 20$$, median = 30, $$Q_3 = 40$$, maximum = 100. Which observation would be considered a suspected outlier?

Accepted Answer

Any value above $$Q_3 + 1.5$$ 	imes ($$Q_3$$ - $$Q_1) = 40 + 1.5$$ 	imes 20 = 70$$

Displaying and Summarizing Quantitative Data & Comparing Distributions

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