model 1 basic average questions Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

Average income of whole group

= ${4200×40+4000×35}/75$

= ${168000+140000}/75$

= $308000/75$ =Rs. 4106$2/3$

Answer: (c)

Sum of first n odd natural numbers = $n^2$

∴ Their average = ${n^2}/n$ = n

∴ Required average = 25

because n = 25

Aliter : Using Rule 7,

Average = 25

Answer: (a)

D’s weight = 80 × 4 – 84 × 3

= 320 – 252 = 68 kg.

E’s weight = 68 + 3 = 71 kg.

Total weight of (A + B + C + D + E)

= 84 × 3 + 68 + 71

= 252 + 68 + 71 = 391 kg.

Total weight of (B + C + D + E)

= 79 × 4 = 316 kg.

∴ A’s weight= 391 – 316 = 75 kg.

Answer: (d)

Using Rule 10,

If the average of '$n_1$' numbers is $a_1$ and the average of '$n_2$' numbers is $a_2$, then average of total numbers $n_1$ and $n_2$ is

$Average = {n_1a_1 + n_2a_2}/{n_1 + n_2}$

Required average

= ${20×30+20×30}/{30+20}$

= ${600+600}/50$

= $1200/50$ = 24

Answer: (c)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

where, $A_1, A_2, A_3, .......... A_n$ are frequencies

Required average

${x_1+x_2+…+x_20}/20$ = ${101×2}/20$

= y-101