Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.

### Examples

The data set {15,0,32,24,0,17,42,0,29,120,0,20}, collected based on minutes spent on homework, has a mode of 0.### Clarifications

*Clarification 1:*Numerical data is limited to positive rational numbers.

General Information

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

**Grade:**6

**Strand:**Data Analysis and Probability

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

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Data
- Mean
- Median
- Mode
- Range

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 5, students interpreted numerical data, with whole-number values, represented with tables or line plots by determining the mean, median, mode and range. In grade 6, students find and interpret mean, median, mode and range given numerical data set with positive rational numbers. In grade 7, students continue building their knowledge while using measures of center and measures of variability to compare two populations.- Instruction includes developing statistical questions that generate numerical data.
- Instruction includes the understanding that data sets can contain many numerical values that can be summarized by one number such as mean, median, mode or range.
- Instruction includes data sets that have more than one mode. Students should understand that a mode may not be descriptive of the data set.
- Instruction includes not only how to calculate the mean, but also what the mean represents
*(MTR.4.1)*. - Instruction focuses on statistical thinking that allows for meaningful discussion of interpreting data
*(MTR.4.1)*. Students should be asked:- What do the numbers tell us about the data set?
- What kinds of variability might need to be considered in interpreting this data?
- What happens when you do not know all the measures in your data set?
- Can you find missing data elements?

- Instruction includes student understanding of the difference between measures of center and measures of variability.
- Instruction includes students knowing when a number represents the spread, or variability, of the data, or when the number describes the center of the data.
- The data set can be represented in tables, lists, sets and graphical representations. Graphical representations can be represented both horizontally and vertically, and focus on box plots, histograms, stem-and-leaf plots and line plots.

### Common Misconceptions or Errors

- Students may incorrectly believe that “average” only represents the mean of a data set. Average may be any of the following: average as mode, average as something reasonable, average as the mean and average as the median.
- Students may confuse mean and median.
- Students may neglect to order the numbers in the data set from least to greatest when finding the median or range.

### Strategies to Support Tiered Instruction

- Teacher discusses with students how the use of the word average in daily life may show a different meaning of the word each time, just as other mathematical words have different meanings in everyday life. This will help students to understand that “average” does not only represent the mean of a data set.
- Teacher provides instruction focused on measures of center, co-creating anchor chart or graphic organizer.
- Teacher provides examples visually that show the clear middle of a data set, but where the average is not the same. This visual will help students understand that the middle of a data set does not mean that amount is the average.
- For example, the figure below shows a data set with mean of 7 and median of 4.

- For example, the figure below shows a data set with mean of 7 and median of 4.

### Instructional Tasks

*Instructional Task 1*Salena has 15 students in her class. The mean shoe size is 8.5. She records the shoe sizes below, with one missing:

**(MTR.4.1, MTR.5.1)**

7.5, 10, 15, 6.5, 7, 9, 9.5, 6, 11, 8.5, 7, 12, 6, 6.5, ___

What shoe size is missing? Explain how she can find the missing shoe size.*Instructional Task 2*

**(MTR.5.1)**Brandi is in the Girl Scouts and they are selling cookies. There are 11 girls in her troop. The median number of boxes of cookies sold by a girl scout is 26, and the range of the number of boxes sold is 30 boxes.

- Part A. What is a possible set of boxes of cookies sold?
- Part B. If the mean number of boxes of cookies sold is 22, describe some possible characteristics of the data set.

### Instructional Items

*Instructional Item 1*

Jonathan works for a sporting goods store, and he is asked to report his sales, in dollars, of running shoes for the week. His numbers are given below.

{150.25, 122.85, 171.01, 118.48, 108.52, 130.15, 154.36}

- Part A. What is the mean?
- Part B. What is the median?
- Part C. If you were Jonathan, which measure would you report and why?

**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.

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

1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))

1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

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

MA.6.DP.1.AP.2a: Use tools to identify and calculate the mean, median, mode and range represented in a set of data with no more than five elements.

MA.6.DP.1.AP.2b: Identify and explain what the mean and mode represent in a set of data with no more than five elements.

## Related Resources

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

## Formative Assessment

## Lesson Plan

## Original Student Tutorial

## Perspectives Video: Expert

## Teaching Ideas

## Tutorial

## Video/Audio/Animation

## MFAS Formative Assessments

Explain Measures of Center:

Students are asked to list measures of center and explain what they indicate about a set of data.

## Original Student Tutorials Mathematics - Grades 9-12

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

## Parent Resources

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