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

Answer: (d)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Required average

${1.11+0.01+0.101+0.001+0.11}/5$

= ${1.332}/5$ = 0.2664

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: (b)

Number of students in the class = x (let)

∴ Number of girls = 50 – x

According to the question,

x × 70 + (50 – x) × 75

= 50 × 72

⇒ 70x + 3750 – 75x = 3600

⇒ 3750 – 5x = 3600

⇒ 5x = 3750 – 3600 = 150

⇒ x = $150/5$ = 30