Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.

### Clarifications

*Clarification 1*: Within the Probability and Statistics course, instruction includes the use of spreadsheets and technology.

General Information

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Data Analysis and Probability

**Standard:**Summarize, represent and interpret categorical and numerical data with one and two variables.

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Categorical Data
- Numerical Data

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students created and interpreted different displays of univariate numerical and categorical data. In grade 8, they created scatter plots and began to interpret them by consider lines of fit. In Algebra I, students interpret the components of data displays for numerical and categorical data, both univariate and bivariate. In later courses, they will use data displays to compare distributions of data sets to one another and to theoretical distributions.- It is the intention of this benchmark to include cases where students must calculate measures of center/variation to interpret
*(MTR.3.1)*. - For students to have full understanding of numerical/categorical, univariate/bivariate data sets and their displays, instruction should include MA.912.DP.1.1. These benchmarks are not intended to be separated. One is reinforced by the other.
- Numerical univariate includes histograms, stem-and-leaf plots, box plots and line plots.
- Numerical bivariate includes scatter plots and line graphs.
- Categorical univariate includes bar charts, line plots, circle graphs, frequency tables and relative frequency tables.
- Categorical bivariate includes segmented bar charts, joint frequency tables and joint relative frequency tables.

- Instruction includes identifying the measures of center and spread from different scenarios.
- Instruction includes explaining that an outlier is extremely smaller or larger than the rest of the data set.
- Teacher provides opportunities to analyze the effects on the measures of center and spread when the outlier is the minimum and maximum.
- This benchmark reinforces the importance of the use of questioning within instruction.
- Does this display univariate or bivariate data?
- Is the data numerical or categorical?
- What do the different quantities within the data display mean in terms of the context of the situational data?

### Common Misconceptions or Errors

- Students may not be able to properly distinguish between numerical and categorical data or between univariate and bivariate data.
- Students may misidentify or misinterpret the quantities in data displays.
- Students may not be able to distinguish between the measures of center (mean, median) and measures of spread (range, IQR).
- Students may not completely grasp the effect of outliers on the data set; or incorrectly conclude a point is an outlier.
- Students may not be able to distinguish the differences between frequencies and relative frequencies.
- Students misidentify the condition that determines a conditional or relative frequency in a joint table.

### Strategies to Support Tiered Instruction

- Instruction includes a graphic organizer to complete collaboratively.
- For example, teacher can provide the graphic below and have students match the vocabulary terminology with the correct definition. Then, have students create an example that can help with remembering the vocabulary terminology.

- For example, teacher can provide the graphic below and have students match the vocabulary terminology with the correct definition. Then, have students create an example that can help with remembering the vocabulary terminology.

- Teacher provides students with definitions and co-creates examples for frequency and relative frequency.
- For example, have students draw a definition chart in their interactive notebook. Give them the opportunity to create an example that will help them remember the definition.

### Instructional Tasks

*Instructional Task 1 ( MTR.3.1, MTR.4.1)*

- The histogram below shows the efficiency level (in miles per gallons) of 110 cars.
- Part A. Does this display univariate or bivariate data?
- Part B. Is the data numerical or categorical?
- Part C. What do the different quantities within the data display mean in terms of the context of the situational data?
- Part D.
- How many cars have an efficiency between 15 and 20 miles per gallon?
- How many cars have an efficiency more than 20 miles per gallon?
- What percentage of cars have an efficiency less than 20 miles per gallon?

*Instructional Task 2 ( MTR.3.1, MTR.4.1) *

- A police department tracked the number of ticket writers and number of tickets issued for each of the past 8 weeks. The scatter plot shows the results.

- Part A. Does this display univariate or bivariate data? Is the data numerical or categorical?
- Part B. What do the different quantities within the data display mean in terms of the context of the situational data?
- Part C. Which statement is an appropriate interpretation of the data?
- a. More ticket writers result in fewer tickets being issued.
- b. There were 50 tickets issued every week.
- c. When there are 10 ticket writers, there will be 600 tickets issued.
- d. When there are more ticket writers, more tickets are being issued.

### Instructional Items

*Instructional Item 1 *

- The scatter plot show the amount of sleep needed per day by age.

- Part A. Does this display univariate or bivariate data? Is the data numerical or categorical?
- Part B. What is a possible trend that is shown by the data?

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

This benchmark is part of these courses.

1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))

7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current))

7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))

1207350: Mathematics for College Liberal Arts (Specifically in versions: 2022 and beyond (current))

1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))

1700600: GEAR Up 1 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))

1700610: GEAR Up 2 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))

1700620: GEAR Up 3 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))

1700630: GEAR Up 4 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))

1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))

7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 - 2023, 2023 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

MA.912.DP.1.AP.2: Given a univariate or bivariate data distribution (numerical or categorical), identify the different components and quantities in the display.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Lesson Plans

## Perspectives Video: Expert

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.