Q: A bar graph shows the number of tickets sold for each type at 1 PM: Child (10), Adult (15), Senior (5). What percentage of tickets sold were for children?

$$\frac{10}{10+15+5} \times 100 = \frac{10}{30} \times 100 = 33.3\%$$

Q: A Pareto chart is constructed from the following data: Error Type 1 (40), Error Type 2 (25), Error Type 3 (15), Error Type 4 (5). What is the percentage of Error Type 2 out of the total errors?

$$\frac{25}{40+25+15+5} \times 100 = \frac{25}{85} \times 100 \approx 29.4\%$$

Question 1

Which of the following best describes the difference between a bar graph and a Pareto chart?

Accepted Answer

A bar graph displays categorical data with bars in any order, while a Pareto chart arranges bars in descending order of frequency.

Question 2

Given the frequency table below, which category would appear first in a Pareto chart?

Ticket Type: Child (23), Adult (44), Senior (36), Member (9)

Accepted Answer

Adult

Question 3

If a bar graph shows the number of students with different hair colors in a classroom, and the frequencies are: Blonde (10), Black (6), Brown (4), Red (2), which hair color would be the last bar in a Pareto chart?

Accepted Answer

Red

Question 4

A movie theater sold the following tickets for the 5 PM showing: Child (20), Adult (25), Senior (15). How many more adult tickets were sold than child tickets?

Accepted Answer

$$25 - 20 = 5$$

Question 5

Which of the following is a key feature of a Pareto chart that distinguishes it from a standard bar graph?

Accepted Answer

Bars are arranged in descending order of frequency.

Question 6

Suppose you are analyzing ticket sales at a movie theater. If the total number of tickets sold at 3 PM is Child (15), Adult (20), Senior (10), what is the proportion of adult tickets sold at that time?

Accepted Answer

$$\frac{20}{15+20+10} = \frac{20}{45} \approx 0.444$$

Question 7

In a Pareto chart of ticket sales, which ticket type would be placed second if the frequencies are: Adult (44), Senior (36), Child (23), Member (9)?

Accepted Answer

Senior

Question 8

A bar graph shows the number of students with each hair color in Classroom A: Blonde (8), Black (5), Brown (7), Red (2). How many more students have brown hair than red hair?

Accepted Answer

$$7 - 2 = 5$$

Question 9

If a Pareto chart is constructed from the following data: Blue (12), Green (8), Yellow (15), Red (5), which color will be the third bar from the left?

Accepted Answer

Green

Question 10

A bar graph shows ticket sales for four showings: 1 PM (Child: 10, Adult: 15, Senior: 5), 3 PM (Child: 15, Adult: 20, Senior: 10), 5 PM (Child: 20, Adult: 25, Senior: 15), 7 PM (Child: 18, Adult: 22, Senior: 12). Which showing sold the most tickets overall?

Accepted Answer

5 PM

Question 11

Which of the following scenarios is most appropriate for using a Pareto chart?

Accepted Answer

Analyzing the most common types of customer complaints in a business.

Question 12

If a bar graph shows the number of tickets sold for each type at 7 PM: Child (18), Adult (22), Senior (12), what is the total number of tickets sold at that time?

Accepted Answer

$$18 + 22 + 12 = 52$$

Question 13

A Pareto chart is used to prioritize issues in a hospital. The frequencies of issues are: Medication errors (30), Patient falls (15), Equipment failures (10), Communication errors (5). Which issue should be addressed first according to the chart?

Accepted Answer

Medication errors

Question 14

In a bar graph, what does the height of each bar represent?

Accepted Answer

The frequency or count of the category.

Question 15

If a Pareto chart is constructed from the following data: Defect A (50), Defect B (30), Defect C (20), Defect D (10), what is the cumulative frequency after the second bar?

Accepted Answer

$$50 + 30 = 80$$

Question 16

A bar graph shows the number of tickets sold for each type at 1 PM: Child (10), Adult (15), Senior (5). What percentage of tickets sold were for children?

Accepted Answer

$$\frac{10}{10+15+5} 	imes 100 = \frac{10}{30} 	imes 100 = 33.3\%$$

Question 17

Which of the following is NOT a correct use of a bar graph?

Accepted Answer

Showing the trend of a variable over time.

Question 18

A Pareto chart is constructed from the following data: Error Type 1 (40), Error Type 2 (25), Error Type 3 (15), Error Type 4 (5). What is the percentage of Error Type 2 out of the total errors?

Accepted Answer

$$\frac{25}{40+25+15+5} 	imes 100 = \frac{25}{85} 	imes 100 \approx 29.4\%$$

Question 19

If you want to highlight the most significant categories in a dataset, which type of chart should you use?

Accepted Answer

Pareto chart

Question 20

A bar graph shows the number of tickets sold for each type at 5 PM: Child (20), Adult (25), Senior (15). What is the ratio of child tickets to senior tickets?

Accepted Answer

$$\frac{20}{15} = 1.33$$

Bar Graphs and Pareto Charts: Visualizing Categorical Data

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