lesson 2 problem solving practice median and mode

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Statistics and probability

Course: statistics and probability   >   unit 3.

• Statistics intro: Mean, median, & mode
• Mean, median, & mode example

Mean, median, and mode

• Calculating the mean
• Calculating the median
• Choosing the "best" measure of center
• Mean, median, and mode review

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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• Grade 6 McGraw Hill Glencoe - Answer Keys

math test scores: 97,85,92,86	Median =
	Mode =

Explanation:

	Median =
	Mode =

Describe the average speeds using the measures of center.

	Mean =
	Median =
	Mode =

Model with Mathematics Refer to the graphic novel frame below for Exercises a-b.

a. Find the median and mode for each team's wins.

	Median:
	Mode:
	Median:
	Mode:

b . Which team had the better record? Justify your response.

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• Inspiration

Fun teaching resources & tips to help you teach math with confidence

Understanding Data: FREE Mean Median & Mode Lesson

Looking for fun, unique, hands on way to introduce and explore measures of center? This FREE mean median & mode lesson uses pennies to analyze and compare measures of center.

Gathering data and then knowing how best to analyze and summarize that data is an important mathematical skill. In this lesson, students use a handful of pennies to explore different measures of center (mean, median and mode) and discuss what might be the best for their data set.

Materials Needed for Mean, Median Mode Investigation:

• Handful of pennies from various years (20-30 pennies)
• Student handout (download at the end of this post)
• If you don’t have pennies, sample data sets are included, but actual pennies are ideal 😉

This step by step math investigation is meant to be an introduction to mean, median and mode, so no prior knowledge is necessary! This could be used with students in 5th grade and up .

Using the Mean Median & Mode Lesson:

This lesson walks students step by step through gathering, organizing and analyzing their set of data ( the years of their pennies ).

Once the pennies are in order, they look at the years to find the mean, median and mode and will see different ways to compare and analyze it.

For instance, they begin by looking at a dot plot .

Later, they stack pennies to find the mode (the most frequent year will form the highest tower).

The mean median & mode lesson ends with discussion questions to help students understand the differences in these measures of center and consider which best fits the data. They will also consider outliers and the effect that might have on the different measures.

This lesson includes teaching tips, sample data and a student handout pages.

Lastly, the investigation ends with a few ‘practice your skills’ problems to put their newly discovered data skills to work.

{Click HERE to go to my shop and  download the Mean Median & Mode lesson!}

I hope you will find this lesson useful!

Looking for Data Analysis for Younger Ones? Try One of These Ideas:

• Taco Tally: Gathering and Analyzing Data
• Graphing the Weather: Tally & Graph Practice

You might also like these more in depth data analysis resources:

• Data Analysis Graphing Calculator Lessons | Grades 6+
• Data Analysis in Grades K-2 | 8 Different Themes to Explore
• Pingback: Teaching Blog Addict

I’m glad you are the Featured Freebie this week on TBA. I missed this last week and it is perfect for my students. Thank you.

I’m so glad you found this helpful Mary! Thanks for stopping by! 🙂

• Pingback: FREE Exploring Data Math Lesson with Printables : Mean, Median, Mode | Free Homeschool Deals ©
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Thanks so much! I can’t wait to use this lesson for my students!

Great! I hope it goes well! 🙂

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PRACTICE PROBLEMS ON MEAN MEDIAN AND MODE

Problem 1 :

Find the (i) mean  (ii) median  (iii) mode for each of the following data sets :

a)  12, 17, 20, 24, 25, 30, 40

b)  8, 8, 8, 10, 11, 11, 12, 12, 16, 20, 20, 24

c)  7.9, 8.5, 9.1, 9.2, 9.9, 10.0, 11.1, 11.2, 11.2, 12.6, 12.9

d)  427, 423, 415, 405, 445, 433, 442, 415, 435, 448, 429, 427, 403, 430, 446, 440, 425, 424, 419, 428, 441

Problem 2 :

Consider the following two data sets :

Data set A : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 12

Data set B : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 20

a)  Find the mean for both Data set A and Data set B.

b)  Find the median of both Data set A and Data set B.

c)  Explain why the mean of Data set A is less than the mean of Data set B.

d)  Explain why the median of Data set A is the same as the median of Data set B

Problem 3 :

The table given shows the result when 3 coins were tossed simultaneously 40 times. The number of heads appearing was recorded.

Calculate the :   a)  mean     b)  median     c)  mode

Problem 4 :

The following frequency table records the number of text messages sent in a day by 50 fifteen-years-olds

a)  For this data, find the : (i) mean   (ii)  median   (iii)  mode

b)  construct a column graph for the data and show the position of the measures of centre (mean, median and mode) on the horizontal axis.

c)  Describe the distribution of the data.

d)  why is the mean smaller than the median for this data ?

e)  which measure of centre would be the most suitable for this data set ?

Problem 5 :

The frequency column graph alongside gives the value of donations for an overseas aid organisation, collected in a particular street.

a)  construct the frequency table from the graph.

b)  Determine the total number of donations.

c)  For the donations find the :  (i)  mean   (ii)  median   (iii)  mode

d) which of the measures of central tendency can be found easily from the graph only ?

Problem 6 :

Hui breeds ducks. The number of ducklings surviving for each pair after one month is recorded in the table.

a)  Calculate the : (i)  mean   (ii)  median   (iii) mode

b)  Is the data skewed ?

c)  How does the skewness of the data affect the measures of the middle of the distribution ?

Answers 

(1)	Mean	Median	Mode
(a)	24	24	No mode
(b)	13.33	11.5	8
(c)	10.32	10	11.2
(d)	428.57	428	415 and 427

Set A Mean  =  7.73 Median  =  7

Set B Mean  =  8.45 Median  =  7

(c)  the mean of A is less than the mean of B.

(d)   median is the same.

(3)  (a)   Mean  =  1.4     (b)   median  =  1  (c)     mode  =  1

(4)  

(a)   (i)   Mean  =  5.74  (ii)     median  =  7  (iii)   mode  =  8

(c)     bimodal data.

The mean takes into account the full range of numbers of text messages and is affected by extreme values. Also, the value which is lower than the median is well below it.

(e)   The median

(5)  

(b)   ∑f  =  30

(c)  (i)   Mean  =  $2.9  (ii)   median  =  $2  (iii)   mode  =  $2

(6)  

(a)  (i)  Mean  =  4.25    (ii)   median  =  5   (iii)   mode  =  5

c)   By observing the graph, the mean is less than the median and mode.

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• → Statistics & Probability

Mean, Median, Mode Lesson Plan

Get the lesson materials.

Mean Median Mode Guided Notes & Doodles | Measures of Central Tendency

Have you ever wondered how to teach mean median and mode in a fun way to your 5th and 6th grade students?

In this lesson plan, students will learn about measures of central tendency and their real-life applications. Through artistic, interactive, guided notes, a doodle & color by number worksheet, and a maze activity, students will gain a comprehensive understanding of mean, median, and mode.

The lesson culminates in a real life example that explores how sports analysts decide which players are performing the best, and which should be replaced based on calculations.

• Type : Lesson Plans
• Grade : 6th Grade
• Standards : CCSS 6.SP.B.5.c , CCSS 6.SP.A.3
• Duration : 2 Hours
• Topic : Statistics & Probability

Learning Objectives

After this lesson, students will be able to:

Define mean, median, and mode

Calculate mean, median, and mode from a given set of data

Understand the application of mean, median, and mode in a real-life application, specifically sports analytics in the context of baseball

Note: This lesson plan doesn't cover range. See "extensions" for ideas!

Prerequisites

Before this lesson, students should be familiar with:

Basic math operations (addition, subtraction, multiplication, and division)

Understand how to arrange numbers in numerical order

Comparing numbers

Colored pencils or markers

Mean, Median, Mode Guided Notes

Key Vocabulary

Measures of central tendency

Introduction

As a hook, ask students if they have ever wondered how sports analysts calculate which players are performing the best and which should be replaced. Explain that measures of central tendency, specifically mean, median, and mode, are used to make these decisions.

Introduce the learning objectives for the lesson plan.

Use the guided notes to introduce mean and how to find it in a data set. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Check for Understanding . Have students walk through the “You Try!” section. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

Use the guided notes to introduce median and how to find it in a data set. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Use the guided notes to introduce mode and how to find it in a data set. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Have students practice finding mean, median, and mode using the maze activity. Walk around to answer student questions.

Fast finishers can dive into Doodle Math maze activity for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of how mean, median, and mode are used in sports analytics, with different sports statistics the correspond to different statistics. Refer to the FAQ for more ideas on how to teach it!

Additional Self-Checking Digital Practice (Pixel Art Google Sheets)

If you’re looking for digital practice for mean, median, and mode, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation. There’s Easter , Valentine’s Day , and year-round Minecraft-themed versions .

Challenge with Range

If you’re looking for practice problems for range, in addition to mean, median, and mode, try my Doodle Math print activity , and Domino Effect collaborative math game .

What is a data set? Open

A data set is a collection of numerical values or other data points.

What are outliers? Open

Outliers are data points that are significantly different from the rest of the data.

What are measures of central tendency? Open

Measures of central tendency are statistical values that represent the center or middle of a data set. Mean, median, and mode are examples of measures of central tendency.

What is the difference between mean, median, and mode? Open

Mean, median, and mode are all measures of central tendency used in statistics.

Mean is the average of the data set, calculated by adding up all the values in a data set and dividing by the number of values.

Median is the middle value in a data set when the values are arranged in order.

Mode is the value that occurs most frequently in a data set.

How do you remember the difference between mean, median, and mode? Open

Mean is the average, median is the middle, and mode is the most frequent.

How do you calculate mean, median, and mode? Open

Mean, median, and mode are calculated in slightly different ways:

To calculate the mean, add up all the values in the data set and divide by the total number of values.

To calculate the median, arrange the values in order and find the middle value. For an even number of values, take the average of the two middle values.

To find the mode, determine which value occurs most frequently in the data set.

If you have a student that needs a video explainer, here’s a helpful Khan Academy video:

How do mean, median, and mode apply to sports analytics? Open

In the context of sports analytics, mean, median, and mode can be used to evaluate player performance based on statistics like on base percentage, batting average, and wins above replacement.

What is batting average in baseball? Open

Batting average is a statistic used in baseball to measure a player's performance at the plate. It is calculated by dividing the number of hits a player has by the number of times they have at-bats. In statistics, batting average is an example of mean, which is a measure of central tendency used to represent the center or middle of a data set.

What is on base percentage in baseball? Open

On base percentage (OBP) is a baseball statistic that measures how often a player reaches base. It is calculated by dividing the total number of times the player has reached base (hits, walks, hit by pitch) by the total number of plate appearances (at-bats, walks, hit by pitch, sacrifice fly). While OBP is technically an example of mean in statistics, as it represents the average rate at which a player reaches base. However, like median, it is less affected by outliers than mean. For example, if a player has an OBP of .500 but only gets on base in one of their ten plate appearances, their median would be .100, whereas their mean would be .500.

What is wins above replacement in baseball? Open

Wins above replacement (WAR) is a baseball statistic that measures a player's value in comparison to a "replacement level" player. A replacement level player is defined as a player who is readily available to be signed from the minor leagues or free agency. WAR is calculated by comparing a player's performance to that of a replacement level player, and then adjusting for the player's position and the park in which they play.

In statistics, WAR is an example of a measure of central tendency called mode, which represents the most common or frequent value in a data set. In the case of baseball, a player's WAR is often used to determine their overall value and contribution to their team.

Want more ideas and freebies?

Get my free resource library with digital & print activities—plus tips over email.

Mean, median, and mode - video lesson

In this 6th grade video lesson, I use three example data sets and distributions to show how the three measures of central tendency - mean, median, and mode - work in each situation.

In the first example, we cannot calculate the mean, but both median and mode work well to describe the distribution.

And in the last situation (about income), the mean is "thrown off" by the large numbers in the data set, and thus it is the median that better describes the central tendency of the distribution.

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