Tag: maths

Questions Related to maths

If each observation is multiplied by $\displaystyle \frac{1}{3}$ then the mean of the new data will de

maths average arithmetic mean of ap introduction to averages means

  1. $\displaystyle \frac{1}{3}$ times

  2. 3 times

  3. $\displaystyle \frac{1}{\sqrt{3}}$ times

  4. $\displaystyle \frac{2}{3}$ times

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Correct Option: A
Explanation:

Let set of data is 9,10,11,17 and 13

Then mean =$\frac{9+10+11+17+13}{5}=\frac{60}{5}$
If Each observation is multiply by $\frac{9+10+11+17+13}{5}=\frac{60}{5}=12$
Then data are $\frac{9}{3},\frac{10}{3},\frac{11}{3},\frac{17}{3}and \frac{13}{3}$
Then sum of data=$\frac{9}{3}+\frac{10}{3}+\frac{11}{3}+\frac{17}{3}+ \frac{13}{3}=\frac{60}{3}=20$
Then new mean of data=$\frac{20}{5}=4$
Then new data mean =$\frac{4}{12}=\frac{1}{3}$ times of old data

The mean of $x, y, z$ is $y$, then $x + z = .............$

maths average arithmetic mean of ap introduction to averages means

  1. $y$

  2. $3y$

  3. $2y$

  4. $4y$

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Correct Option: C
Explanation:

Mean of 3 numbers $=\dfrac {\mbox {Sum of three numbers}}{3}$

$\Rightarrow y = \dfrac {x+y+z}{3}$

$\Rightarrow 3y=x+y+z$

$\Rightarrow x+z = 2y$

The arithmetic mean of first five natural number is

maths average arithmetic mean of ap introduction to averages means

  1. $2$

  2. $3$

  3. $4$

  4. $8$

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Correct Option: B
Explanation:

$Arithmetic\ mean=\cfrac{1+2+3+4+5}{5}$
$=3$

The arithmetic mean between $2+\sqrt {(2)}$ and $2-\sqrt {(2)}$ is

maths average arithmetic mean of ap introduction to averages means

  1. $2$

  2. $\sqrt {(2)}$

  3. $0$

  4. $4$

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Correct Option: A
Explanation:

Since, the arithmetic mean between $a$ and $b$ is $\displaystyle  \frac {a+b}{2}$
$\therefore $the arithmetic mean between $2+\sqrt 2$ and $2-\sqrt 2$  $=\displaystyle \frac {2+\sqrt 2+2-\sqrt 2}{2}$

$=\dfrac {4}{2}$

$=2$
Option A is correct.

Find the arithmetic mean of the progression $2, 4, 6, 8, 10.$

maths average arithmetic mean of ap introduction to averages means

  1. $10$

  2. $20$

  3. $30$

  4. $6$

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Correct Option: D
Explanation:

Using the formula for Required arithmetic mean $=\dfrac{\text{sum of the terms}}{\text{number of terms}}$


After substituting the values we get$=\dfrac{2+4+6+8+10}{5}=\dfrac{30}{5}=6$

What is the arithmetic mean of the progression $11, 22, 33, 44, 55, 66, 77?$

maths average arithmetic mean of ap introduction to averages means

  1. $44$

  2. $208$

  3. $308$

  4. $48$

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Correct Option: A
Explanation:

Using the formula for required arithmetic mean $=\dfrac{\text{sum of the terms}}{\text{number of terms}}$


After substituing the values we get: $=\dfrac{11+22+33+44+55+66+77}{7}$

                                                $\quad \quad \quad =\dfrac{11(1+2+3+4+5+6+7)}{5}=\dfrac{11\cdot 28}{7}=11\cdot 4=44$

Find the arithmetic mean of first $10$ natural numbers.

maths average arithmetic mean of ap introduction to averages means

  1. $55$

  2. $550$

  3. $5.5$

  4. None of the above

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Correct Option: C
Explanation:

Arithmetic mean of first 10 natural numbers is:

$=\dfrac{1+2+3+4+5+6+7+8+9+10}{10}$
$=\dfrac{(\dfrac{n.(n+1)}{2})}{10}$,  where $n=10$. 
$=\dfrac{(\dfrac{10.11}{2})}{10}$
$=5.5$                                             

Find  AM  of  first $250$  natural numbers.

maths average arithmetic mean of ap introduction to averages means

  1. $115$

  2. $225$

  3. $125$

  4. $125.5$

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Correct Option: D
Explanation:

Sum of first 250 natural numbers:

$S=\dfrac{n(n+1)}{2}=\dfrac{250\times 251}{2}$
$\therefore A.M.=\dfrac{S}{n}=\dfrac{250\times 251}{250\times 2}=125.5$

If $n^{th}$ term of AP is $4n+1$, then AM of $11^{th}$ to $ 20^{ th}$ terms is 

maths average arithmetic mean of ap introduction to averages means

  1. $61.5$

  2. $63$

  3. $63.5$

  4. $62$

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Correct Option: B
Explanation:

Given: $t _{n}=4n+1$

$A.M.=\cfrac{t _{11}+t _{20}}{2}$
           $=\cfrac{4\times 11+1+4\times 20+1}{2}$
           $=63$

If  $n^{th}$ term of AP is $t _n=4n+1$. Find mean of first $10$ terms.   

maths average arithmetic mean of ap introduction to averages means

  1. $85$

  2. $95$

  3. $23$

  4. $7.5$

Show answer
Correct Option: C
Explanation:
Given:
$t _{n}=4n+1$
$\therefore A.M.=\dfrac{\sum _{n=1}^{10}4n+1}{n}$
               $=\dfrac{2n(n+1)+n}{n}$
               $=2n+3$
               $=2\times 10+3$
               $=23$