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

Answer: (b)

Temperature on 4th day

= (4 × 25 + 4 × 25.5 –25.2 × 7)°C

= (100 + 102 – 176.4)°C

= 25.6°C

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

Numbers are : 10, 15, 20, 25, 30, 35, 40, 45

Sum = 220

Average = $220/8$ = 27.5

Answer: (c)

Using Rule 1,

${x_1+x_2+…x_n}/n$ = $\ov{x}$

∴ $??{i=1}?n $$(x_i - \ov{x})$

= $(x_1 - \ov{x})$+$(x_2 - \ov{x})$+…$(x_n - \ov{x})$

= $({x_1+x_2+…+x_n})$ - n.$\ov{x}$

=n $({x_1+x_2+…+x_n}/n)$ - n.$\ov{x}$

= $n\ov{x} – n\ov{x}$ = 0

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: (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)

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