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Unit 2 · Standard 6.DS.4

Describe Data Using the Mean

Lesson 2-8 · Learn It — how the math works

Why we're learning this

Every week, Miguel walks dogs after school to earn money, and he keeps his earnings in a notebook. Across 4 days he earned $60 in all — but not the same amount each day. Later this lesson you'll help Sofia, who tracks her points every basketball game and wants to finish the season averaging 15 points per game.

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What is the mean?

The mean, or average, is a measure of center that describes a whole data set with one number. It is what every value would be if the total were leveled out and shared equally.

Picture itSee what the math looks like before you read about it

Every week, Miguel walks dogs after school to earn some money. He keeps track of his earnings in his notebook. Over 4 days he earned $60 in all. How can Miguel describe his earnings on a typical day?
Where you see this in real lifeEvery week, Miguel walks dogs after school to earn some money. He keeps track of his earnings in his notebook. Over 4 days he earned $60 in all. How can Miguel describe his earnings on a typical day?

Watch me solve itI do — read one step at a time

The problem looks like this
Tape diagram: 60 counters shared equally among 4 days, 15 on each day.6015Day 115Day 215Day 315Day 4
  1. Miguel's 4 days of earnings are shown with counters. When I combine all of the counters, there are 60 of them, which Miguel earned $60 in all.
  2. Now I redistribute the 60 counters equally among the 4 days. Each of the 4 groups ends up with 15 counters.
  3. The arithmetic does exactly the same thing: I find the total, 60, and divide it by the number of days, 4. So 60 ÷ 4 = 15.60 ÷ 4 = 15
  4. We can use $15 to describe Miguel's typical daily earnings. That leveled value is the .

Watch out — mistakes students make here

  • 10 is another value from the list, and it is below the leveled amount once you divide the total by 4.
  • 12 is one of the values in the list; picking a value from the data is not the same as leveling all of them.
  • 44 is the total of the four values — the mean needs that total divided by 4.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. New : a dog walker earns $9, $11, $16, and $12 over 4 days. First, what is the total?
  2. Next, how many values are in the ?
    Check this step
    That number is what we divide by.
  3. Last, divide the total by 4. Is your answer bigger than the smallest day and smaller than the biggest day?
    Check this step
    It should be.

On your ownYou do — solve this one by yourself

Solve: Sofia wants to 15 points per game over 10 games. How many points does she need in all 10 games combined?

My answer

Stuck? Open one hint at a time.

Hint 1

Undo the mean: the mean was found by dividing a total by the count, so the total comes back by doing the opposite.

Hint 2

Imagine every one of the 10 games landed exactly on 15 points. What would the season total be?

Hint 3

Use 15 points per game, ten times over.

Check my answer
✅ Answer: 150 points
If every one of the 10 games hit the target of 15 points, the total would be 15 × 10 = 150 points. That is the total she needs for a mean of 15.

Turn & TalkSay it out loud with a partner

Miguel earned $60 walking dogs over 4 days. What does the question when it asks what he earns on a 'typical day'?

Try starting with:

  • A typical day means Miguel earned ___ each day.Un día típico significa que Miguel ganó ___ cada día.
  • To share $60 equally across 4 days I would ___.Para repartir $60 en partes iguales entre 4 días yo ___.
Use these wordsmeanaveragetypicalequallydata set