Tag: introduction to averages

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Multiple choice maths average arithmetic mean of ap introduction to averages means

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?

  1. $Rs\ 14000$
  2. $Rs\ 7000$
  3. $Rs\ 9950$
  4. $Rs\ 4875$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratios 2:3:4:5. M = 2x = 8000, so x = 4000. Total = (2+3+4+5)x = 14x = 14 * 4000 = 56000. Average = 56000 / 4 = 14000.

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $cosec1^o$
  2. $sec1^o$
  3. $cot1^o$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a complex trigonometric series sum. The arithmetic mean of the given series is indeed cosec(1 degree).

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $49$
  2. $50$
  3. $51$
  4. $52$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $200.5-150.5=50$

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $19$
  2. $\displaystyle 17\frac{1}{2}$
  3. $\displaystyle 20\frac{1}{2}$
  4. $22$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Common difference d = (10 - 28) / (11 + 1) = -18 / 12 = -1.5. The 6th A.M. is a + 6d = 28 + 6(-1.5) = 28 - 9 = 19.

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. 7

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The no .of  observations is $3+5=8$

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

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  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. $\left(\dfrac{n+1}{2}\right)-1 \left(\dfrac{2n+1}{3}\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer