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Grade 5 (age 10-11)

grade 5 Average & Likelihood

The average (mean) is what each one gets when several values are shared out evenly, so it stands for the whole set of data. Add all the values and divide by how many there are; going the other way, the average times the number of values gives back the total. Even when classes have different numbers of students, averages let you compare which class read more books. Change the value for each weekday to move the average line on the bar graph; the picture below takes from the tall bars and fills the short ones until they are all the same height.

What Is an Average?

⚖️ Sharing Evenly Gives the Average
①The starting values from Monday to Friday are 8, 4, 6, 10 and 7, which add up to 35
②Sharing 35 evenly over 5 days gives 7 a day, and that 7 is the average
③Some bars rise above the average line and some fall below it
④The amounts above the average and the amounts below it add up to the same total
8
4
6
10
7

Averaging Means Sharing Evenly

💡 Taking from the High, Filling the Low
①Take the extra from the bars that are above the average
②Give it to the bars that are below the average
③Then all five bars are the same height, and that height is the average
④In the picture, ↓ marks a bar that gives some away and ↑ marks a bar that needs filling

Summary

Finding the Average
Average = sum of valuesnumber of values
Add all the values, then divide by how many there are
Finding the Total
Total = average × number of values
If you know the average and how many values there are, you can find the total
🎯 Summary
①Average = sum of values ÷ number of values
②The average stands for the whole set of data
③The amount above the average equals the amount below it
④Two sets can have the same average but be spread out differently
⑤How likely something is can be described in words: impossible, unlikely, even chance, likely, certain

Examples and Unit Test

Example 1
Five students have 8, 6, 10, 9 and 7 books. What is the average number of books?
1
First find the sum: 8 + 6 + 10 + 9 + 7 = 40.
2
There are 5 students, so 40 ÷ 5 = 8 books.
▸ 8 books
Some students have more than 8 and some fewer, but shared evenly each would have 8.
Example 2
A set of 4 values has an average of 6. What is the sum of the values?
1
Sum = average × number of values.
2
6 × 4 = 24, so the sum is 24.
▸ 24
The average is an even share, so putting the shares back together gives the total.
Unit Test
What is the average of 5, 6, 8, 9 and 7?
①6
②7
③8
④35
▸ ② 7
1
Find the sum: 5 + 6 + 8 + 9 + 7 = 35.
2
There are 5 values, so 35 ÷ 5 = 7.
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