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6th grade (Eureka Math/EngageNY)

Unit 6: Lesson 2

Topic B: Summarizing a distribution that is approximately symmetric using the mean and mean absolute deviation
Math
6th grade (Eureka Math/EngageNY)
Module 6: Statistics
Topic B: Summarizing a distribution that is approximately symmetric using the mean and mean absolute deviation
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Calculating the mean

Google Classroom
Learn how to calculate the mean by walking through some basic examples & trying practice problems.
The mean is used to summarize a data set. It is a measure of the center of a data set. Let's look at an example.
Claire has 5 cookies, Brooke has 3 cookies, Deandra has 6 cookies, and Lucy has 2 cookies. Find the mean number of cookies.
Let's start by drawing a picture to show each person and their cookies:
Imagine that the girls combined all of their cookies
and then each took the same number of cookies.
Each girl would have 4 cookies. So, the mean is 4 cookies.
Key idea: We can think of the mean as the number of cookies each girl would have if they were equally distributed among the four girls.
Find the mean number of bananas each of the monkeys has in the picture below.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
bananas

Calculating the mean

We don't need to draw a picture every time we want to calculate the mean. Instead, we can follow these steps:
Step 1: Add up all of the data points (this is like combining all of the cookies)
Step 2: Divide the total by the number of data points in the data set (this is like each girl taking the same number of cookies)
Let's do this for the data set left brace, 7, comma, 2, comma, 8, comma, 6, comma, 7, right brace:
7+2+8+6+7=30Step 1305=6Step 2\begin{aligned} 7 + 2+ 8 + 6 + 7&= \blueD{30} &\small{\gray{\text{Step 1}}} \\\\\\\\ \dfrac{\blueD{30}}{5} &= 6&\small{\gray{\text{Step 2}}}\end{aligned}
The mean of this data set is 6.

Calculating the mean walkthrough

Let's find the mean of the data set left brace, 2, comma, 1, comma, 2, comma, 4, comma, 5, comma, 4, right brace together.
Add up all of the data points.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

How many data points are in the data set?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Great! Now divide the total by the number of data points.
The mean of this data set is
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
.

Now it's time to try some practice on your own.

Practice

Find the mean of the data set left brace, 5, comma, 23, comma, 8, comma, 12, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Find the mean of the data set left brace, 2, comma, 7, comma, 5, comma, 4, comma, 6, comma, 3, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Find the mean of the data set left brace, 4, point, 5, comma, 5, comma, 3, point, 5, comma, 2, comma, 2, point, 5, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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  • purple pi teal style avatar for user Tamera Jarvis
    Posted 6 years ago. Direct link to Tamera Jarvis's post “how would you know when a...”
    how would you know when an outlier affects a data set?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • winston default style avatar for user gabeisbest
      Posted 2 years ago. Direct link to gabeisbest's post “An outlier is a number th...”
      Good Answer
      An outlier is a number that is far from the data set. This could be the case such as in this set:
      158, 156, 85, 145, 157, 159. 85 is the outlier. Without the 85 the mean would be 155, but with the 85 the mean is about 143. Just one number makes the mean decrease by 12. An outlier always affects a data set, because an outlier is a number that is nowhere near the current set of numbers.
      (24 votes)
  • mr pink red style avatar for user hannah.manter
    Posted 2 years ago. Direct link to hannah.manter's post “this are so hard sorry I'...”
    this are so hard sorry I'm not good with math
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    • purple pi teal style avatar for user Camille A. T.
      Posted 2 years ago. Direct link to Camille A. T.'s post “I would suggest keeping a...”
      Great Answer
      Good Answer
      I would suggest keeping a notebook with all the math facts you have learned. Try to really get stuff pounded into your brain before you move on. For this you can use the rhyme: Hey diddle didle, the medians the middle, you add and divided for the mean, the mode is the one that appears the most, and the range is the difference between. Never skip stuff or guess randomly. Try to make sure you REALLY understand the answer. It might take a bit longer, but it's worth it in the long run. Also, don't be afraid to ask for help. I struggle with math, too. But just keep trying and I promise you'll get it. Also, just take a deep breath. It can get hard if you're super stressed. And I like to type out what I'm thinking, so if there is a problem, my teacher can figure out where I went wrong and correct it from there. Keep it up!
      (27 votes)
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    My teacher gives me this one like eighty times a day so I know all the answers but she still keeps giving it to me. >_<
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    Posted 5 years ago. Direct link to kyrathechampion's post “Can there be more than on...”
    Can there be more than one mode?
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    • winston default style avatar for user gabeisbest
      Posted 2 years ago. Direct link to gabeisbest's post “As you probably know, mod...”
      As you probably know, mode is the biggest set of ungrouped data. If two sets of data have the same amount, but the other data is less than the data that they have, then both of them are the modes. This is also true with 3 modes, 4 modes, 5 modes and so on.
      (3 votes)
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    Posted 8 months ago. Direct link to shubhankar.saha's post “Thanks for the lesson Kha...”
    Thanks for the lesson Khan because I am learning 5th grade math so l can avoid summer slide in fourth grade summer.😋😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀
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    i dont understand this stuff AT ALL. I dont think i have been taught this yet to,and if i have i just dont understand it,and need someone to go over it with me. So i understand for next time.So my question is... can u help me with this and show me how to do it again, and go over it with me please. thank you if u get this. because idk where this message is going or to who.
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