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Course: Statistics and probability > Unit 3

Lesson 1: Measuring center in quantitative data
Math
Statistics and probability
Summarizing quantitative data
Measuring center in quantitative data
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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 3/5
  • 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
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 {7,2,8,6,7}:
7+2+8+6+7=30Step 1305=6Step 2
The mean of this data set is 6.

Calculating the mean walkthrough

Let's find the mean of the data set {2,1,2,4,5,4} together.
Add up all of the data points.
  • 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

How many data points are in the data set?
  • 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

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 3/5
  • 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
.

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

Practice

Find the mean of the data set {5,23,8,12}.
  • 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

Find the mean of the data set {2,7,5,4,6,3}.
  • 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

Find the mean of the data set {4.5,5,3.5,2,2.5}.
  • 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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  • purple pi teal style avatar for user Tamera Jarvis
    Posted 8 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?
    (79 votes)
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    • winston default style avatar for user gabeisbest
      Posted 3 years ago. Direct link to gabeisbest's post “An outlier is a number th...”
      Incredible Answer
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      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.
      (68 votes)
  • piceratops ultimate style avatar for user Lim, Ryan
    Posted 7 years ago. Direct link to Lim, Ryan's post “How about the range? What...”
    How about the range? What is it?
    (25 votes)
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    • female robot grace style avatar for user Shubham Agarwal
      Posted 7 years ago. Direct link to Shubham Agarwal's post “The range of a numerical ...”
      Incredible Answer
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      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.
      (79 votes)
  • mr pink red style avatar for user hannah.manter
    Posted 3 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
    (10 votes)
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    • leafers tree style avatar for user Camille A. T.
      Posted 3 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!
      (47 votes)
  • male robot hal style avatar for user Hybrid
    Posted 5 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. >_<
    (22 votes)
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  • duskpin seed style avatar for user kyrathechampion
    Posted 6 years ago. Direct link to kyrathechampion's post “Can there be more than on...”
    Can there be more than one mode?
    (10 votes)
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    • winston default style avatar for user gabeisbest
      Posted 3 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.
      (9 votes)
  • duskpin ultimate style avatar for user Nelaski
    Posted a year ago. Direct link to Nelaski's post “How do I find a missing n...”
    How do I find a missing number when I know the mean?
    (10 votes)
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    Posted a year ago. Direct link to dulcelyzpena's post “A little challenging”
    A little challenging
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    Posted a year ago. Direct link to cheryl.gabatin's post “what is median?”
    what is median?
    (6 votes)
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  • scuttlebug blue style avatar for user Arcadia Soto, Paulina
    Posted 9 months ago. Direct link to Arcadia Soto, Paulina's post “so much easier now that I...”
    so much easier now that I have practiced
    (9 votes)
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  • aqualine tree style avatar for user Jae'dyn F
    Posted a year ago. Direct link to Jae'dyn F's post “this is going to help me ...”
    this is going to help me a lot
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      Posted a year ago. Direct link to 40s.isterrett's post “⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀...”
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      Answer dukes.clynton:)'s post “⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀...”
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      (3 votes)