## Objective

Define and determine the median of a data set.

## Common Core Standards

### Core Standards

The core standards covered in this lesson

6.SP.A.2— Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

### Statistics and Probability

6.SP.A.2— Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.B.5.C— Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

### Statistics and Probability

6.SP.B.5.C— Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

- Understand the
**median**of a data set as the middle value that separates the data set into two parts with the same number of data values below and above the median. - Understand that the median is a value from the data set when there are an odd number of values, and it is
*not*a value in the data set when there are an even number of values. - Determine the median of data sets.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

In Lessons 6 and 7, students learn two other measures of central tendency, median and mode. Recall with students their conversations earlier in the unit around the idea of “center”, and how there were a range of values that appropriately represented “center”, not just one exact value. Extend this idea to explain that there are three common ways to think about the center of a data set (mean, median, mode), each one determined in a different way.

### Lesson Materials

- Number strips (1 per student) — These require some cutting, which can either be done prior to the lesson or during the lesson if scissors are provided to the students. Note, the same strips are used for both Lesson 6 and Lesson 9.

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

### Problem 1

a.The weather in the beginning of March has varied over the last several days. You’re interested in knowing what a typical temperature of a day in early March is. To do this, you decide to find out what temperature is in the middle of the data set when it’s ordered from least to greatest.

**Temperatures of the first 11 days in March (°F)**

24 35 64 60 35 21 31 38 49 57 50

- Using Paper Strip A, order the temperatures from least to greatest, writing one number in each box.
- Fold the paper strip in half so that half of the temperatures are on the left side and half of the temperatures are on the right side.
- What temperature is in the middle? What is the median temperature of the first 11 days of March?

b.Looking at the upcoming weather report, there are predicted temperatures for the rest of the month. The list below shows the predicted temperatures for the last 10 days in March.

**Predicted temperatures of the last 10 days in March (°F)**

50 49 49 49 49 48 48 46 46 48

- Using Paper Strip B, repeat the activity using the predicted temperatures for the last 10 days in March.
- What temperature is in the “middle” of the data set? What is the median predicted temperature of the last 10 days in March?

#### Guiding Questions

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### Problem 2

One-pound bags of baby carrots are sold in the grocery store. Depending on the size of the carrots, the number of carrots in a bag can vary. The dot plot below shows the number of baby carrots in a sample of 16 one-pound bags from the grocery store.

What is the median number of carrots in a one-pound bag at the grocery store?

#### Guiding Questions

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### Problem 3

Create a data set of at least 10 numbers such that:

- All of the numbers in the data set are whole numbers.
- The median is not a whole number.
- The median is not part of the data set.

#### Guiding Questions

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#### References

Open Middle *Median with Constraints*

*Median with Constraints* by Daniel Luevanos is made available on Open Middle under the CC BY-NC-SA 4.0license. Accessed April 3, 2018, 1:59 p.m..

Modified by Fishtank Learning, Inc.

## Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

Fishtank Plus Content

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## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

### Problem 1

Explain how you would find the median of a data set with 15 values in it.

### Problem 2

The dot plot below shows the scores on a math test. Find the median test score.

### Student Response

An example response to the Target Task at the level of detail expected of the students.

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## Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

- Include error analysis problems where data sets are not ordered from least to greatest before the median is found.
- Include problems where students find the mean and the median of the same data set.

- Open Middle
*Mean, Median, and Range* - Open Up Resources
*Grade 6 Unit 8 Practice Problems*—Lesson 13 - EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 12—Lesson 12 (Problem Set)

Lesson 5

Lesson 7