how would you know when an outlier affects a data set?

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.

How about the range? What is it?

The range of a numerical set is just the difference of the largest and smallest numbers. For example, lets say we have a set: {1, 4, 2, 9, 10} We will take the largest number, 10, and the smallest number, 1, and find the difference. 10-1=9. Therefore, the range of the set is 9. Hopefully this helps you understand range any better.

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. >_<

Your teacher wants you to be very proficient in this I guess but now you can do it in a snap

Can there be more than one mode?

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.

this are so hard sorry I'm not good with math

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!

Main content

6th grade

Course: 6th grade > Unit 11

Lesson 4: Mean and median

Calculating the mean

Q: 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. >_<

Your teacher wants you to be very proficient in this I guess but now you can do it in a snap

Q: Can there be more than one mode?

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.

Q: this are so hard sorry I'm not good with math

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!

CCSS.Math:

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.

bananas

[I need help! Please show me the solution.]

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:

$\begin{aligned} 7 + 2+ 8 + 6 + 7&= \blueD{30} &\small{\gray{\text{Step 1}}} \\\\\\\\ \dfrac{\blueD{30}}{5} &= 6&\small{\gray{\text{Step 2}}}\end{aligned}$

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.

[Show solution]

How many data points are in the data set?

[Show solution]

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
.

[Show solution]

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.

[Show solution]

Find the mean of the data set left brace, 2, comma, 7, comma, 5, comma, 4, comma, 6, comma, 3, right brace.

[Show solution]

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.

[Show solution]

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Tamera Jarvis
Posted 7 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?
Button navigates to signup pageComment on Tamera Jarvis's post “how would you know when a...”
(56 votes)
Answer
- gabeisbest
  Posted 2 years ago. Direct link to gabeisbest's post “An outlier is a number th...”
  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.
  Comment on gabeisbest's post “An outlier is a number th...”
  (40 votes)
Lim, Ryan
Posted 6 years ago. Direct link to Lim, Ryan's post “How about the range? What...”
How about the range? What is it?
Button navigates to signup pageComment on Lim, Ryan's post “How about the range? What...”
(18 votes)
Answer
- Shubham Agarwal
  Posted 6 years ago. Direct link to Shubham Agarwal's post “The range of a numerical ...”
  The range of a numerical set is just the difference of the largest and smallest numbers. For example, lets say we have a set: {1, 4, 2, 9, 10} We will take the largest number, 10, and the smallest number, 1, and find the difference. 10-1=9. Therefore, the range of the set is 9. Hopefully this helps you understand range any better.
  Comment on Shubham Agarwal's post “The range of a numerical ...”
  (58 votes)
Hybrid
Posted 4 years ago. Direct link to Hybrid's post “My teacher gives me this ...”
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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(18 votes)
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- Trever
  Posted 2 years ago. Direct link to Trever's post “Your teacher wants you to...”
  Your teacher wants you to be very proficient in this I guess but now you can do it in a snap
  Comment on Trever's post “Your teacher wants you to...”
  (8 votes)
21
Posted a month ago. Direct link to 21's post “This is easy but khan aca...”
This is easy but khan academy is such a help, VOte up for thank you
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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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- Camille A. T.
  Posted 2 years ago. Direct link to Camille A. T.'s post “I would suggest keeping a...”
  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!
  Comment on Camille A. T.'s post “I would suggest keeping a...”
  (30 votes)
Anthony
Posted a month ago. Direct link to Anthony's post “⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀...”
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⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀
⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄
Button navigates to signup pageComment on apayne29's post “⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀...”
(10 votes)
Answer
kyrathechampion
Posted 5 years ago. Direct link to kyrathechampion's post “Can there be more than on...”
Can there be more than one mode?
Button navigates to signup pageComment on kyrathechampion's post “Can there be more than on...”
(5 votes)
Answer
- 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.
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  (4 votes)