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Shortcut 16:

\( A=\frac{Q_{1+}Q_{2+}Q_{3+….+}Q_n}N\)

A = Average; N = Number of elements;
Q = Quantity of element
Question:
Find the average of 23, 25, 30, 36, and 42.
Answer:
Q1+Q2+Q3+Q4+Q5 = 23 + 25 + 30 + 36 + 42
= 156
N = 5
A = 156/5 = 31.2

Shortcut 17:

   \(A=\frac SN \)

A = Average; S = Sum of quantities;
N = Number of elements
Question:
Sum of marks scored by 20 students in a class is 450. Find the average mark of the class.
Answer:
S = 450

N = 20
A = 450/20
= 22.5

Shortcut 18:

If every element is increased by a certain number,the average also increased by same

Question:
Average age of a family of four members is 34. What is the average age of the family after 4 years?
Answer:
Since every ones age is increased by four in 4 years, the average will also increase by 4
The new average = 34 + 4 = 38
Proof:
Total age of the family before 4 years = 34 x 4 = 136
Total increased age for four members = 4 x 4 = 16
New total age = 136 + 16 = 152
New average = 152/4 = 38

Shortcut 19:

Quantity of removed of added element

\( A_1N_{1\sim}A_2N_2\)

A1 = Initial average; A2 = Final Average
N1 = Initial no.of elements
N2 = Final no.of elements
Question:
The average weight of 10 students in class was 45kg. After adding one more student to the class, the average became 44.5. What is the weight of the new student?
Answer:
A1 = 45; A2 = 44.5
N1 = 10; N2 = 11
Substitute the values in the above formula.
Weight of new student = 45×10~ 44.5×11
= 39.5 kg