Tag: arithmetic mean of ap

Questions Related to arithmetic mean of ap

If the total incomes of $M,N,O,P$ are in the rate a $2:3:4:5$ and the total income of $M$ is $Rs\ 8000$ , then find approximate average salary of all four?

maths average arithmetic mean of ap introduction to averages means

  1. $Rs\ 14000$

  2. $Rs\ 7000$

  3. $Rs\ 9950$

  4. $Rs\ 4875$

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Correct Option: A

The artimetic mean of $2 sin 2^o, 4 sin 4^o, 6sin6^o,...,180sin 180^o$ is equal to 

maths average arithmetic mean of ap introduction to averages means

  1. $cosec1^o$

  2. $sec1^o$

  3. $cot1^o$

  4. None of these

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Correct Option: A

Arithmetic Mean is ______ affected by extreme values.

maths average arithmetic mean of ap introduction to averages means

  1. Not

  2. Highly

  3. Less

  4. None of these

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Correct Option: A

Suppose a population $A$ has $100$ observations $101,102...200$ and other population $B$ has $100$ observations $151,152...250$. 

Find the difference in their means

maths average arithmetic mean of ap introduction to averages means

  1. $49$

  2. $50$

  3. $51$

  4. $52$

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Correct Option: B
Explanation:

The observations of $A$ are $101,102,......,200$

The sum is $\dfrac{100}{2}[2(101)+(100-1)1]\50(202+99)\50(301)=15050$
Mean is $\dfrac{15050}{100}\150.5$
The observations of $B$ are $151,152,......,250$
The sum is $\dfrac{100}{2}[2(151)+(100-1)1]\50(302+99)\50(401)=20050$
Mean is $\dfrac{20050}{100}=200.50$
The difference is $200.5-150.5=50$

The mean of 2, 7, 6 and x is 15 and the mean of 18, 1, 6, x and y is 10. What is the value of y ?

maths average arithmetic mean of ap introduction to averages means

  1. $-5$

  2. $-10$

  3. $-20$

  4. $-30$

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Correct Option: C
Explanation:

$\dfrac{2+7+6+x}{4}=15$


$15+x=60$

$x=45$

Now,
$\dfrac{18+1+6+45+y}{5}=10$

$70+y=50$

$y=-20$

Sum of $50$ A.M. between $20$ and $30$ is :

maths average arithmetic mean of ap introduction to averages means

  1. $1255$

  2. $1205$

  3. $1250$

  4. $1225$

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Correct Option: A

$11\,AM's$ are inserted between $28$ and $10$ then ${6}^{th}\,AM$ is 

maths average arithmetic mean of ap introduction to averages means

  1. $19$

  2. $\displaystyle 17\frac{1}{2}$

  3. $\displaystyle 20\frac{1}{2}$

  4. $22$

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Correct Option: A

The mean of $3$ observations is $12$ and mean of $5$ observations is $4$ the combined mean is 

maths average arithmetic mean of ap introduction to averages means

  1. 7

  2. 8

  3. 9

  4. 10

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Correct Option: A
Explanation:

The no .of  observations is $3+5=8$

The sum of observations is $3(12)+5(4)=36+20=56$
The mean is $\dfrac{56}{8}=7$

The sum of $9$ numbers is $246$. If the average of three of them is $24$, what is the average of the remaining numbers?

maths average arithmetic mean of ap introduction to averages means

  1. $30$

  2. $29$

  3. $31$

  4. $25$

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Correct Option: A

A boy draws n squares with sides $1,2,3,4,5....$ in inches.The average area covered by these n squares  will be:  

maths average arithmetic mean of ap introduction to averages means

  1. $\left(\dfrac{n+1}{2}\right)$

  2. $\left(\dfrac{n+1}{2}\right)\left(\dfrac{2n+1}{3}\right)$

  3. $\left(\dfrac{n+1}{2}\right)\left(\dfrac{2n+1}{3}\right)^{-1}$

  4. $\left(\dfrac{n+1}{2}\right)-1 \left(\dfrac{2n+1}{3}\right)$

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Correct Option: A