Question

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.

1. describe how histograms and stem-and-leaf plots are similar. they both display the distribution of a dataset. they show the frequency of data values in different groups

1. 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?

1. 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

Explanation:

Question 3

Histograms and stem - and - leaf plots are both used to represent the distribution of a dataset. A histogram uses bars to show the frequency of data values within different intervals (or bins). A stem - and - leaf plot separates each data value into a stem (usually the leading digit or digits) and a leaf (the trailing digit). Both of these visualizations allow us to see how often different values (or ranges of values) occur in the data, giving us an idea about the shape of the data distribution (such as if it is symmetric, skewed, etc.) and the spread of the data.

Erskine is collecting data on the percentage of the US population aged 65 or older for every decade since 1900. A line graph would be appropriate here. A line graph is used to show how a variable changes over time. In this case, the independent variable is time (each decade since 1900) and the dependent variable is the percentage of the population aged 65 or older. By plotting the percentage on the y - axis and the decade (or year) on the x - axis and connecting the points with a line, we can easily see the trend (whether the percentage is increasing, decreasing, or staying relatively constant) over time.

1. Bar Graph: A bar graph can be used to compare the population of different cities. We can have the cities on the x - axis and the population (in millions or the given number) on the y - axis. Each bar represents a city, and the height of the bar represents the population of that city. This allows for a quick visual comparison of the population sizes of the five cities.
2. Pie Chart (with some considerations): A pie chart can be used to show the proportion of each city's population to the total population of these five cities. First, we need to calculate the total population of the five cities ($33200000 + 17800000+17700000 + 17500000+17400000=103600000$). Then, for each city, we calculate the percentage of its population relative to the total (e.g., for Tokyo/Yokohama: $\frac{33200000}{103600000}\times100\%\approx32.05\%$). The pie chart will show the relative contribution of each city to the total population of these five cities. However, pie charts are best when we want to show proportions, while bar graphs are better for direct comparison of magnitudes.
3. Table (already given, but as a display): The given table is also a data display that shows the city, country, and population clearly. It is useful for looking up the exact population values of each city.

Answer:

Both histograms and stem - and - leaf plots display the distribution of a dataset by showing the frequency of data values in different groups (or intervals for histograms, and through the organization of stems and leaves for stem - and - leaf plots). They help in understanding the spread, shape, and frequency of occurrence of data values.

Question 4