model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Average of all numbers

= ${30×40+40×30}/70$

= $240/7$ = 34$2/7$

Aliter : Using Rule 10,

Here, $n_1$ = 30, $a_1$ = 40

$n_2$ = 40, $a_2$ = 30

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

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 mean

= ${1×1+2×2+3×3+4×4+5×5+6×6+7×7}/{1+2+3+4+5+6+7}$

= ${1+4+9+16+25+36+49}/28$

= $140/28$ = 5

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

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

The required average marks

= ${55×50+60×55+45×60}/{55+60+45}$

= ${2750+3300+2700}/{160}$

= $8750/160$ = 54.68

Answer: (a)

Value of 13th result

= 25 × 20 – 12 × 15 – 12 × 18

= 500 – 180 – 216 = 104

Answer: (c)

Sum of 4 new numbers

= 50 ×104 – 100 × 44

= 5200 – 4400 = 800

∴ Average = $800/4$ = 200

Aliter : Using Rule 19,

Here, N = 100, T = 44

n = 4, y = 50 – 44 = 6

∴ Average of new numbers

= T+ $({N/n}+1)$

= 44+ $({100/4}+1) ×6$

= 44 + 26 × 6

= 44 + 156 = 200

Answer: (a)

Weight of B = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight

= 40 × 2 + 43 × 2 – 45 × 3

= 80 + 86 – 135

= 166 – 135 = 31 kg