Q: Which formula correctly calculates the relative frequency for a category?

$$ \text{Relative Frequency} = \frac{\text{Frequency of the category}}{\text{Total number of observations}} $$

Q: A survey of 100 students found that 40 prefer coffee, 35 prefer tea, and 25 prefer juice. What angle should the 'tea' sector be in a pie chart?

$$ \frac{35}{100} \times 360^{\circ} = 126^{\circ} $$

Question 1

Which of the following best describes 'raw data' in the context of statistics?

Accepted Answer

Data collected from a survey or experiment that has not yet been organized.

Question 2

A frequency distribution is used to:

Accepted Answer

List each category of data and the number of occurrences for each category.

Question 3

Which formula correctly calculates the relative frequency for a category?

Accepted Answer

$$ 	ext{Relative Frequency} = \frac{	ext{Frequency of the category}}{	ext{Total number of observations}} $$

Question 4

Why is it important to use relative frequencies instead of frequencies when comparing groups of different sizes?

Accepted Answer

Relative frequencies allow for direct comparison regardless of group size.

Question 5

Which of the following is NOT a correct step in constructing a bar graph for qualitative data?

Accepted Answer

Use the area of each rectangle to represent the frequency.

Question 6

A pie chart is most appropriate for displaying:

Accepted Answer

The distribution of a single categorical variable as parts of a whole.

Question 7

Suppose you have the following data on favorite breakfast cereals by manufacturer: Kellogg's (8), General Mills (5), Post (3), Quaker (4). What is the relative frequency of General Mills?

Accepted Answer

$$ \frac{5}{20} = 0.25 $$

Question 8

When constructing a side-by-side bar graph to compare two groups, why should you use relative frequencies instead of frequencies?

Accepted Answer

Because the groups may have different sample sizes, making frequencies misleading.

Question 9

Which of the following statements about pie charts is TRUE?

Accepted Answer

Each sector's area is proportional to the frequency of the category it represents.

Question 10

A survey of 100 students found that 40 prefer coffee, 35 prefer tea, and 25 prefer juice. What angle should the 'tea' sector be in a pie chart?

Accepted Answer

$$ \frac{35}{100} 	imes 360^{\circ} = 126^{\circ} $$

Question 11

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

Accepted Answer

A bar graph uses the height of rectangles to represent frequency, while a pie chart uses the area of sectors.

Question 12

If a frequency distribution table for favorite colors shows: Red (10), Blue (15), Green (5), what is the relative frequency for Blue?

Accepted Answer

$$ \frac{15}{30} = 0.5 $$

Question 13

Which scenario best illustrates when a side-by-side bar graph should be used?

Accepted Answer

Comparing the distribution of favorite sports between male and female students.

Question 14

A researcher collects data on the preferred mode of transportation (car, bus, bike, walk) for 200 people. Which graphical summary would best show the proportion of each mode?

Accepted Answer

Pie chart

Question 15

Which of the following is NOT a reason to organize qualitative data into tables or graphs?

Accepted Answer

To ensure the data is not lost.

Organizing Qualitative Data: Tables, Bar Graphs, and Pie Charts

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