# MA.4.DP.1.2

Determine the mode, median or range to interpret numerical data including fractional values, represented with tables, stem-and-leaf plots or line plots.

### Examples

Given the data of the softball team’s hat size represented on a line plot, determine the most common size and the difference between the largest and the smallest sizes.

### Clarifications

Clarification 1: Instruction includes interpreting data within a real-world context.

Clarification 2: Instruction includes recognizing that data sets can have one mode, no mode or more than one mode.

Clarification 3: Within this benchmark, data sets are limited to an odd number when calculating the median.

Clarification 4: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Line Plot
• Median
• Mode
• Range
• Stem-and-Leaf Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to introduce concepts of mode, median, and range as measures of center and spread in a set of data. This work builds on interpreting different kinds of graphs with numerical and categorical data in grade 3 (MA.3.DP.1.2). The mean as a measure of center is introduced in grade 5 (MA.5.DP.1.2).
• Instruction includes providing students multiple opportunities to organize their data (MA.4.FR.1.4). During instruction it is important for students to organize their data from least to greatest which will help them determine:
• range by subtracting the least value from the greatest value in the set.
• mode by finding the value that occurs most often.
• median by finding the value in middle of the set.
• For example, fifteen students were asked to rate how much they like fourth grade on a scale from one to ten. Here is the data collected: 1, 10, 9, 6, 5, 10, 9, 8, 3, 3, 8, 9, 7, 4, 5. The first step is to put the data in ascending order.
• 1, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10. The median is 7, the mode is 9 and the range is 9.

### Common Misconceptions or Errors

• Students sometimes have difficulty understanding that there may be no mode or more than one mode of a data set. Examples should be given to explicitly teach this concept.
• Students may confuse the range with the number of data points.

### Strategies to Support Tiered Instruction

• Instruction includes providing a data set that may have no mode or more than one mode.
• For example, for the data set 2, 3, 5, 7, 9, 11, there is no mode.
• For example, for the data set 2, 2, 3, 5, 5, 7, 9, 11, 11, the modes are 2, 5, and 11.
• Instruction includes providing the data set on index cards or sticky notes. Students then move the data set in order from least to greatest. For numbers that repeat, students stack the numbers on top of each other. This helps with understanding if there is no mode, or more than one mode.
• Example:
• Instruction includes opportunities to find the range on a line plot. Students subtract the least value on the line plot with an X from the greatest value with an X.
• Example:
• Instruction includes showing how to cover up the data points in the middle of the line plot so that only the first and last data points are shown. This allows students to focus on the values that will be used to calculate the range.
• Example:

Measure the length of 10 used pencils in the class to the nearest $\frac{\text{1}}{\text{8}}$inch.
• Part A. Create a stem-and-leaf plot and a line plot to represent the length of all ten pencils.
• Part B. From your completed line plot, find the median, range and mode of your data set.

### Instructional Items

Instructional Item 1

The line plot below shows all of the results of the sum of two six-sided dice.
Number of Ways to Roll a 2, 3, 4 ... with a Pair of Dice
What is the mode of the data on the line plot?
• a. 12
• b. 10
• c. 7
• d. 6

*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.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.DP.1.AP.2: Determine the mode or range to interpret numerical data including fractional values, represented with tables or line plots. Data set to include only whole numbers and halves. Limit the greatest and least number in a data set to a whole number.

## Related Resources

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

## Lesson Plans

Motion for Speed:

Students will investigate the relationships between the initial speed of a car and the distance required for it to stop.  Students will record their results onto a student guide to determine how a car moving faster or slower affects its ability to stop.  Finally, students will investigate why we have different speed limits on different roads in this integrated lesson plan.

Type: Lesson Plan

Exploring Mode:

In this lesson plan, students will practice finding the mode of a set of data and recognizing how it is used in real life situations. Students will be given the opportunity to collect data, create line plots, interpret the numbers, and find the mode of the data.

Type: Lesson Plan

## Perspectives Video: Teaching Idea

Using Visual Models to Determine Mode, Median and Range:

Unlock an effective teaching strategy for teaching median, mode, and range in this Teacher Perspectives Video for educators.

Type: Perspectives Video: Teaching Idea

## Teaching Ideas

Ball Bounce Experiment:

Students investigate different balls' abilities to bounce and represent the data they collect graphically.

Type: Teaching Idea

Jump or Be Lunch! SeaWorld Classroom Activity:

Students will predict how high they can jump and then compare the height of their jumps to how high a rockhopper penguin can jump out of the water. They will practice mathematical skills for determining averages.

Type: Teaching Idea

## 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.