multiple-choice questions
use the information provided in each question to determine your answer(s). diagrams are not necessarily drawn to scale.
1. suppose that your algebra i teacher creates a box-and-whisker plot of your class’s most recent test scores. which statistic cannot be read from the data display?
a. the lowest score
b. the median score
c. the highest score
d. the score that occurs most frequently
2. a student conducts a survey where she asks all the high school sophomores their height to the nearest inch. which of the following would be appropriate to display the results of her survey? select all that apply.
a. histogram
b. stem-and-leaf plot
c. box-and-whisker plot
d. line graph

open-response questions
use the information provided to answer the questions in this part. clearly indicate all your steps, and include substitutions, diagrams, graphs, charts, etc., as needed. diagrams are not necessarily drawn to scale.
3. describe how histograms and stem-and-leaf plots are similar.
4. erskine uses a website to collect data on the percentage of the united states population that is age 65 or older. he finds the percentage for every decade since 1900. which type of display should he use for this information? why?
5. the table lists the five cities with the highest populations in the world. list the types of data displays that would be appropriate for displaying this information. justify your answer.
city/urban area | country | population
tokyo/yokohama | japan | 33,200,000
new york metro | usa | 17,800,000
são paulo | brazil | 17,700,000
seoul/inchon | south korea | 17,500,000
mexico city | mexico | 17,400,000
source: citymayors.com/statistics

Question

multiple-choice questions
use the information provided in each question to determine your answer(s). diagrams are not necessarily drawn to scale.
1. suppose that your algebra i teacher creates a box-and-whisker plot of your class’s most recent test scores. which statistic cannot be read from the data display?
a. the lowest score
b. the median score
c. the highest score
d. the score that occurs most frequently
2. a student conducts a survey where she asks all the high school sophomores their height to the nearest inch. which of the following would be appropriate to display the results of her survey? select all that apply.
a. histogram
b. stem-and-leaf plot
c. box-and-whisker plot
d. line graph

open-response questions
use the information provided to answer the questions in this part. clearly indicate all your steps, and include substitutions, diagrams, graphs, charts, etc., as needed. diagrams are not necessarily drawn to scale.
3. describe how histograms and stem-and-leaf plots are similar.
4. erskine uses a website to collect data on the percentage of the united states population that is age 65 or older. he finds the percentage for every decade since 1900. which type of display should he use for this information? why?
5. the table lists the five cities with the highest populations in the world. list the types of data displays that would be appropriate for displaying this information. justify your answer.
city/urban area | country | population
tokyo/yokohama | japan | 33,200,000
new york metro | usa | 17,800,000
são paulo | brazil | 17,700,000
seoul/inchon | south korea | 17,500,000
mexico city | mexico | 17,400,000
source: citymayors.com/statistics

Accepted Answer

### Question 1 (Multiple - Choice)
# Brief Explanations:
A box - and - whisker plot shows the minimum (lowest score), maximum (highest score), median, and the first and third quartiles. The mode (score that occurs most frequently) is not shown in a box - and - whisker plot.
# Answer:
D. The score that occurs most frequently

### Question 2 (Multiple - Choice)
# Brief Explanations:
- **Histogram**: Can be used to show the frequency distribution of height (a continuous - like variable when measured to the nearest inch).
- **Stem - and - Leaf Plot**: Can be used to display the individual data points of height in an organized way, showing the distribution.
- **Box - and - Whisker Plot**: Can show the five - number summary (minimum, first quartile, median, third quartile, maximum) of the height data.
- **Line Graph**: Is used to show change over time, and height of sophomores is not a time - related variable, so it's not appropriate.
# Answer:
A. Histogram, B. Stem - and - Leaf Plot, C. Box - and - Whisker plot

### Question 3 (Open - Response)
# Brief Explanations:
1. Both histograms and stem - and - leaf plots are used to represent the distribution of a dataset.
2. They both can show the frequency of data values within different intervals or groupings. For example, in a stem - and - leaf plot, the stem can be thought of as a category or interval, and the leaves show the number of data points in that "interval". In a histogram, the bars represent the frequency of data in each interval. Also, both can give an idea about the shape of the data distribution (e.g., symmetric, skewed).
# Answer:
Both histograms and stem - and - leaf plots display the distribution of a dataset. They show the frequency of data values in groups/intervals, helping to visualize the shape (e.g., symmetric, skewed) of the data. The stem - and - leaf plot shows individual data points in a grouped way, while the histogram uses bars for intervals, but both convey how often different values occur.

### Question 4 (Open - Response)
# Brief Explanations:
## Step1: Analyze the data type
The data is the percentage of the US population aged 65 or older for every decade since 1900. So we have two variables: time (decades since 1900) and the percentage.
## Step2: Choose the appropriate display
A line graph is appropriate. Because a line graph is used to show the change in a variable (the percentage of the population aged 65 or older) over time (decades since 1900). It can clearly show the trend (increase, decrease, or stability) of the percentage as time progresses.
# Answer:
Erskine should use a line graph. This is because a line graph is ideal for showing how a variable (the percentage of the US population aged 65 or older) changes over time (every decade since 1900). It can effectively display trends in the data.

### Question 5 (Open - Response)
# Brief Explanations:
## Step1: Analyze the data
We have data about cities, their countries, and their populations.
## Step2: Choose appropriate displays
- **Bar Graph**: We can use a bar graph to compare the populations of the five cities. Each bar can represent a city, and the height of the bar can represent the population. This allows for easy visual comparison of the population sizes.
- **Table**: The data is already in a table, and a table is a good way to present the exact values of city, country, and population for clear reference.
- **Pie Chart (if we consider relative population)**: If we want to show the relative proportion of each city's population to the total population of these five cities, a pie chart can be used. But since the question is about appropriate displays, bar graph and table are very appropriate. Justifying the bar graph: It shows the population of each city visually, making it easy to compare which city has a larger or smaller population. Justifying the table: It presents the data in an organized way with exact values for city, country, and population.
# Answer:
- **Bar Graph**: Appropriate because it allows for easy visual comparison of the populations of the five cities. Each bar represents a city, and the height of the bar corresponds to the city's population.
- **Table**: Appropriate as it presents the data (city, country, population) in an organized, easy - to - read format with exact values.
- (Optional) **Pie Chart**: If we want to show the relative proportion of each city's population to the total population of these five cities, a pie chart can be used. But bar graph and table are more direct for this data as we may be more interested in comparing the absolute population sizes.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1 (Multiple - Choice)

Answer:

Question 2 (Multiple - Choice)