Q: How is the area for each category in a pie chart calculated?

$$\text{Relative frequency observed per category} \times 360^\circ$$

Question 1

Which of the following best describes a frequency distribution for a categorical variable?

Accepted Answer

A tabular summary showing the number of observations in each of several nonoverlapping categories.

Question 2

Given a sample of 50 soft drink purchases with 19 Coke Classic, 8 Diet Coke, 5 Dr. Pepper, 13 Pepsi-Cola, and 5 Sprite, what is the relative frequency of Pepsi-Cola purchases? Use the formula $$	ext{Relative frequency} = \frac{	ext{Frequency in the class}}{n}.$$

Accepted Answer

$$0.26$$

Question 3

Which of the following statements about bar charts and pie charts is TRUE?

Accepted Answer

Bar charts display frequencies, relative frequencies, or percentage frequencies for categorical data.

Question 4

How is the area for each category in a pie chart calculated?

Accepted Answer

$$	ext{Relative frequency observed per category} 	imes 360^\circ$$

Question 5

Using Sturges' rule, what is the approximate number of classes for a data set with $$n = 40$$ observations? Use $$1 + 3.3 \log(n)$$ and round to the nearest integer.

Accepted Answer

$$1 + 3.3 \log(40) \approx 6.1$$, so 6 classes

Question 6

If the range of a quantitative data set is 28 and you want to use 7 classes, what is the approximate class width? Use $$	ext{Class width} = \frac{	ext{range}}{	ext{number of classes}}.$$

Accepted Answer

$$28 \div 7 = 4$$

Question 7

Which of the following is a key difference between a histogram and a bar chart?

Accepted Answer

Bar charts have separated bars, while histograms have adjacent bars representing continuous intervals.

Question 8

A histogram of audit times is shown to be skewed to the right. What does this indicate about the distribution of audit times?

Accepted Answer

Most audit times are short, with a few very long times (outliers on the right).

Question 9

Given the following cumulative frequency distribution for audit times (in days): $$(10-15] = 6$$, $$(15-20] = 7$$, $$(20-25] = 4$$, $$(25-30] = 2$$, $$(30-35] = 1$$, what is the cumulative frequency for audits completed in 25 days or less?

Accepted Answer

$$17$$

Question 10

If 85% of audits are completed in 25 days or less, and there are 20 audits in total, how many audits took more than 25 days?

Accepted Answer

$$0.15 	imes 20 = 3$$

Question 11

Which of the following is NOT an advantage of a stem-and-leaf display compared to a histogram?

Accepted Answer

It is better for displaying large data sets with many digits.

Question 12

In a cross-tabulation table, what do the rows and columns typically represent?

Accepted Answer

Rows and columns each represent a variable, with cells showing the frequency for each combination.

Question 13

Which graphical method is most appropriate for displaying the relationship between two quantitative variables?

Accepted Answer

Scatter diagram

Question 14

A scatter diagram shows a downward trend from left to right. What type of relationship does this indicate?

Accepted Answer

Negative linear relationship

Question 15

If a cumulative percentage frequency distribution shows 65% of values are less than or equal to 20, and 95% are less than or equal to 30, what percentage of values are between 20 and 30?

Accepted Answer

$$95\% - 65\% = 30\%$$

Question 16

Which of the following best describes an OGIVE?

Accepted Answer

A line graph plotting cumulative frequencies against upper class limits.

Question 17

In a right-inclusive class interval $$(a, b]$$, which values are included?

Accepted Answer

Values greater than $$a$$ and less than or equal to $$b$$

Question 18

A pie chart for soft drink purchases shows Coke Classic at 38%. What angle does this sector occupy in the pie chart? Use $$	ext{Angle} = 	ext{Relative frequency} 	imes 360^\circ.$$

Accepted Answer

$$0.38 	imes 360^\circ = 136.8^\circ$$

Question 19

Which of the following is a correct interpretation of a cumulative relative frequency of $$0.85$$ for a class interval?

Accepted Answer

85% of the data values are less than or equal to the upper class limit.

Summarising Data: Tabular & Graphical Methods

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