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.
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.
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?
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?