Average
What is
the average of 6, 11, 7?
Average is like you are "flattening
out" the numbers -> sharing total values equally
Why Use Average
(1) It is a “central” value of a sample set.
(2) It is “fair sharing”, pulled by up large values and brought down by the smaller values.
Step 1: Total Value : Add
all the values of the numbers -> 6+7+11 = 24
Step 2: Count of Data = 3 (there are
3 numbers - 6, 11, 7)
Step 3: Divide
the Total Value by the Number of Data
Average = 24/3 = 8
Formula
Average = Total Amount/Value/Quantity/Set
of numbers
Count of shares/items
Example:
A dice is
thrown 10 times. The following results are obtained:
5, 5, 1, 2, 6, 4, 2, 3, 4, 1
What is
the average score?
Step 1: Total Value
=5+5+1+2+6+4+2+5+4+1 = 35
Step 2: Count = 10
Step 3: Average = 35/10 = 3.5
Example:
What is the average of 5, 8 and 11?
Step 1: Total Value = Add
the numbers: 5 + 8 + 11 = 24
Step 2: how many numbers (i.e. we added 3 numbers) =3
Step 3: Average = 24/ 3 = 8
Step 2: how many numbers (i.e. we added 3 numbers) =3
Step 3: Average = 24/ 3 = 8
Example:
Five students have the following number of sweets:
A: 9
B: 2
C: 7
D: 4
E: 3
a. What is the number of sweets that each can have for equal sharing? (Average)
Average = 9 + 2+ 7 + 4 + 3
5
5
= 25/5
= 5
b. Who has the most sweets? (mode)
Student A
c. What is percent of sweets that Student B has?
Percent = Number of sweets of Student B x 100
Total Number
= 2 x 100
25
25
= 8%
d. Both Student B and C gave away their sweets. What fractions of the total number of sweets have been given away?
Sweets given away = 2 + 3
25
25
= 1/5
e. What is the new average?
Average = 9 + 0 + 7 + 4 + 0
5
5
= 20 /5
= 4 sweets
Practice
Find the average
:
(1) 12, 15,
24 and 13 (12+15+24+13) / 4 =16
(2) 34, 56 and 33 (34+56+33) / 3 = 41
(3) 36cm,
47cm, 38cm and 51cm (36+47+38+51) / 4 = 43
AVERAGE COMPUTATION – WORD PROBLEM
Average = Total Value
Count of Data
Method:
Step 1: Total Value : Add
all the values of the numbers -> 6+7+11 = 24
Step 2: Count of Data = 3 (there are
3 numbers - 6, 11, 7)
Step 3: Use the Average Formula
Example
10 textbooks
cost $6 each and 20 notebooks cost $2 each.
What is the average cost of each item ?
What is the average cost of each item ?
Step1: Total Value = (10 x $6) + (40
x $2) = $60 + $80 = $240
Step2: Count of Data = 10 + 40 = 50
Step 3: Average = total value /
items = $240 / 50 = $4.80
Example
Mary
bought 4 skirts at $65 each and 1 blouse at $45 each.
What was the average cost of the items ?
What was the average cost of the items ?
Total
Value = (4x $89) + (1x$45) = 
$305
Number of items = 5
Average
= $305/5 =
$61$305Number of items = 5
COMPLEX AVERAGE WORD
PROBLEMS
The more
complex Average Computation questions usually involve 2 objects with different
their average values, or to find a specific average of 1 object with the
information from another object.
The
average-table is to help learners understand how the value of different objects
are related when using the average formula. That is, it is to be used as a
working table to determine the linkage of an unknown value and given data via
the average formula.
It may
seem complicated, but it is the average formula (for more than 1 data) in table
form.
The Average-Table
Object?
|
Value
of 1 data or average value
|
Count
|
Total
Value
|
Average of all items
|
Item1
|
A
|
B
|
AxB
|
(AxB) + (CxD)
|
Item2
|
C
|
D
|
CxD
|
(B+D)
|
Combined Total
|
B+D
|
(AxB) +
(CxD)
|
How to fill in the table? Example/Explanation:
The average
height of 8 men is 1.72m. If one of them is 1.6m tall,
what is
the total height of the other 7 men?
The
object is usually the item with the number count,
Example: 8 men, 4 pens,
5 books
The items are men, pens, books, and
the number count is 8,4,5.
Value = Value of each of the object.
Total value = Each Value x Count or
Average value x Count
-> the average of an item can be used to compute the total value of
specified item
Average of all items = Sum of Total
Value/Total Count.
Method:
Step1: Draw table and fill in information from question
Step2: Let U be the missing value/required value
Step3: Use the average formula to find the answer
Step2: Let U be the missing value/required value
Step3: Use the average formula to find the answer
Example:
Step 1: Fill
in the table with the information from the question
object?
|
Value/Avg
|
Count
|
Total
value
|
Average
Price
|
7 men
|
7
|
U
|
1.72
|
|
1 man
|
1.6
|
1
|
1.6
|
|
Total
|
8
|
U + 1.6
|
Step2: Let U be the value missing
Let U be the total height of the 7
men
Step3: Use average formula to find the
answer
Total Height of 8 men = Average
height x Total number
U + 1.6 = 1.72 x 8
U = 12.16
Total height of the other men = 12.16m
Example
The
average length of 6 ropes is 168 cm. The average length of 4 of the ropes is
172cm. What is the total length of the other two ropes ?
Step 1: Draw
and fill table
Obj
|
Val/Avg
|
Count
|
Total
|
Average
|
4ropes
|
4
|
172 x 4
|
168
|
|
2 rope
|
2
|
U
|
||
Total
|
6
|
172x4 +
U
|
Step2: Let U be the total length of
the other 2 ropes
Total length of the other 2 ropes -> Total length of 6 ropes – Total length of 4
ropes
Step3: Use formula to find the answer
172x4 + U = 168 x 6
U = 320cm
The total
length of the other 2 ropes is 320cm.
Practice: (when doing question – Draw the
Average-Table at the working area)
The
average mass of 9 children is 42kg. If the masses of 3 of them are 37kg, 46kg
and 42 kg, what is the average mass of the other 6 children? Express your
answer to 1 decimal place.
Val/Avg
|
Count
|
Total Mass
|
Average mass
|
|
3 C
|
3
|
37+46+42
|
42
|
|
6 C
|
U
|
6
|
6U
|
|
Total
|
9
|
6U + 125
|
Total mass = 9 x 42= 378kg
37+46+42 = 125kg
Let U be the average mass of 6 children
6U + 125 = 378
6U = 253
U = 42.2 kg
The average mass of 6 children is
42.2 kg
~~~~ END ~~~~ :)