Unit Review: Florida - Data Displays & Interpretation

The student counselors at your school are analyzing how study habits might affect academic performance. They conducted a survey asking students two questions:

• How many hours per week do you spend completing Algebra 1 assignments?

• What was your final grade in Algebra 1?

Which of the following is the most appropriate graph to represent the relationship between the two variables in this data set?

• Scatter plot because it involves numerical variables. 

• Bar graph because it involves categorical variables. 

• Box plot because it involves numerical variables.

• Stem-and-leaf plot because it involves categorical variables.

  Stem-and-leaf plot because it involves categorical variables. - no response given

Answer explanation

A scatter plot is the most appropriate graph for this data set because it displays the relationship between two numerical variables: hours spent on assignments and final grades in Algebra 1.

The student council at FLCCA is working on a school-wide data project to better understand student habits and preferences. They collected the following data sets:

• Data Set A: favorite school club (Art, Choir, or Dance)

• Data Set B: preferred learning style (Visual, Auditory, or Kinesthetic)

Which of the following is the most appropriate graph to represent the relationship between the two variables in this data set?

• Circle graph because it involves a univariate categorical variable.

• Line graph because it involves bivariate numerical variables.

• Segmented bar chart because it involves bivariate categorical variables. 

• Frequency table because it involves a univariate numerical variable.

Answer explanation

The correct choice is a segmented bar chart because it effectively represents the relationship between two categorical variables: favorite school club and preferred learning style.

At FLCCA, the librarian wants to encourage reading. She tracks how many books each student reads in a month. After collecting the data from 250 students, she wants to see how reading habits vary across the school.

Select the words that correctly finish the statement below: 

The most appropriate method to represent the data above would be a 

• histogram

• bivariate

• numerical

• categorical

Answer explanation

The data collected on the number of books read by students is numerical, as it involves counting. A numerical method is best to represent this data, allowing for analysis of reading habits across the school.

Organize these options into the right categories

Groups:

(a) Numerical

,

(b) Categorical

,

(c) Bivariate

,

(d) Univariate

• salaries of employees

• Blue, brown, grey

• hours and test scores

• box and whisker plot

Select the words that correctly finish the statement below for the line plot shown. 

• data represents one variable

• data is classified as univariate

• data applies to numbers

• data set is numerical

Answer explanation

The correct choices indicate that the data in the line plot represents one variable, is classified as univariate, applies to numbers, and is numerical, all of which are characteristics of a line plot.

Tags

CCSS.3.MD.B.4

A recent study found that schools with more math tutors tend to have higher math passing rates. Based on this information, which of the following best explains the relationship between the number of tutors and passing rates?

• Tutors directly cause students to pass

• Passing rates cause schools to hire more tutors

• There is a correlation between the number tutors and passing rates, but this does not necessarily mean one causes the other.

• Students only pass because they see a tutor

Answer explanation

The study indicates a correlation between the number of tutors and passing rates, but this does not imply that one directly causes the other. Other factors may influence both variables.

Tags

CCSS.HSS.ID.C.9

A research team analyzed two scenarios:

• Neighborhoods with more parks per square mile tend to report higher levels of physical activity among residents.

• After a city introduced a tax on sugary drinks, there was a measurable decrease in the average daily sugar consumption among its population.

Which of the following best explains the difference between these two observations?

• Both observations demonstrate causation because they are based on observed changes.

• The parks data shows correlation, while the sugary drink tax suggests causation due to a direct policy intervention and observed effect.

• The parks data proves causation, while the sugary drink tax only shows correlation.

• Both observations only show correlation, not causation.

Answer explanation

The parks data shows correlation since higher park density correlates with physical activity, but does not imply causation. In contrast, the sugary drink tax indicates causation due to a direct policy change leading to reduced sugar consumption.

Tags

CCSS.HSS.ID.C.9

A city introduced two health initiatives:

• Average cholesterol levels before and after a new nutrition curriculum was added (numerical data).

• Proportion of students who exercise regularly before and after gym class became mandatory (categorical data).

Which statement best describes what can be concluded from these results?

• Both results indicate correlation, but causation cannot be confirmed due to possible confounding variables.

• The nutrition curriculum data demonstrates causation, but the gym class data only shows correlation.

• Only the gym class policy proves causation because participation is required for all students.

• Both results prove causation because the changes were directly followed by measurable improvements.

Answer explanation

Both health initiatives show changes, but without controlled studies, we can't confirm causation due to potential confounding variables. Thus, the correct conclusion is that both results indicate correlation.

Tags

CCSS.HSS.ID.C.9

A city council wants to estimate how many residents in the city use public transportation to commute to work. A random sample of 250 residents is surveyed, and 75 residents say they use public transportation.

If there are 8,000 residents in the city, what is the best estimate of the total number of residents who use public transportation to commute to work?

• 2,400

• 2,800

• 3,000

• 3,200

Answer explanation

To estimate the total users, calculate the proportion of the sample: 75 out of 250 use public transport, or 0.3. Multiply this by the total population: 0.3 * 8000 = 2400. Thus, the best estimate is 2,400.

Tags

CCSS.7.RP.A.2C

A university wants to estimate the average number of hours students spend studying each week. A random sample of 500 students is surveyed, and the average reported study time is 7.5 hours per week, with a margin of error of ±0.8 hours.

The university has a total enrollment of 25,000 students.

What is the estimated total number of hours all students at the university spend studying each week?

• 187500

• 200000

• 37500

• 312500

Answer explanation

To find the total study hours, multiply the average study time (7.5 hours) by the total enrollment (25,000 students). This gives 7.5 * 25,000 = 187,500 hours, which is the correct answer.

Tags

CCSS.HSS.IC.B.4