Q: If a frequency table has the following counts: Red (15), Blue (25), Green (10), what is the percentage of Green observations?

$$ \frac{10}{50} \times 100 = 20\% $$

Q: Which formula would you use to calculate the proportion of observations in a category?

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

Q: If a survey of 200 people finds that 60 prefer tea, 80 prefer coffee, and 60 prefer juice, what is the percentage of people who prefer coffee?

$$ \frac{80}{200} \times 100 = 40\% $$

Question 1

Which of the following best describes a frequency distribution in statistics?

Accepted Answer

A summary table showing the number of observations in each category.

Question 2

Suppose you have a dataset of students' favorite fruits: apples, bananas, oranges, and grapes. If you want to show how many students chose each fruit, which statistical tool should you use?

Accepted Answer

Frequency table

Question 3

Given the following frequency table for survey responses: Yes (30), No (50), Maybe (20). What is the proportion of 'No' responses?

Accepted Answer

$$ \frac{50}{100} = 0.5 $$

Question 4

A bar chart is used to display which type of data?

Accepted Answer

Categorical data

Question 5

If a frequency table has the following counts: Red (15), Blue (25), Green (10), what is the percentage of Green observations?

Accepted Answer

$$ \frac{10}{50} 	imes 100 = 20\% $$

Question 6

Which of the following is a key step when constructing a frequency table from raw data?

Accepted Answer

Sort the data into categories and count the number of observations in each.

Question 7

A Pareto chart is a type of bar graph where categories are arranged in which order?

Accepted Answer

Decreasing frequency

Question 8

If you have a frequency table with the following counts: A (12), B (8), C (20), what is the cumulative frequency for category C?

Accepted Answer

$$ 12 + 8 + 20 = 40 $$

Question 9

Which formula would you use to calculate the proportion of observations in a category?

Accepted Answer

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

Question 10

A researcher collects data on the types of vehicles passing through an intersection: Car (40), Truck (15), Motorcycle (5). What is the relative frequency of Trucks?

Accepted Answer

$$ \frac{15}{60} = 0.15 $$

Question 11

Which of the following statements about a Pareto chart is TRUE?

Accepted Answer

It helps identify the most significant categories by ordering them from highest to lowest frequency.

Question 12

In a frequency table, the sum of all frequencies should equal:

Accepted Answer

The total number of observations

Question 13

If a survey of 200 people finds that 60 prefer tea, 80 prefer coffee, and 60 prefer juice, what is the percentage of people who prefer coffee?

Accepted Answer

$$ \frac{80}{200} 	imes 100 = 40\% $$

Question 14

Which of the following is NOT a correct use of a frequency table?

Accepted Answer

To display the distribution of continuous data without grouping

Question 15

A frequency table for favorite colors shows: Blue (25), Red (15), Green (10). What is the cumulative frequency after Red?

Accepted Answer

$$ 25 + 15 = 40 $$

Question 16

If the frequency of a category is 18 and the total number of observations is 90, what is the proportion for that category?

Accepted Answer

$$ \frac{18}{90} = 0.2 $$

Question 17

Which of the following best describes the purpose of calculating relative frequency?

Accepted Answer

To compare the frequency of a category to the total number of observations

Question 18

A bar chart differs from a histogram in that:

Accepted Answer

A bar chart displays categorical data, while a histogram displays continuous data.

Question 19

If a frequency table for types of pets shows: Dog (40), Cat (30), Bird (10), Fish (20), what is the percentage of Fish?

Accepted Answer

$$ \frac{20}{100} 	imes 100 = 20\% $$

Question 20

Which of the following is the correct way to construct a Pareto chart from a frequency table?

Accepted Answer

Arrange categories in decreasing order of frequency and plot their frequencies as bars.

Descriptive Statistics: Frequency Distributions and Bar Charts

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