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

Arithmetic Mean is ______ affected by extreme values.

  1. Not

  2. Highly

  3. Less

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

The arithmetic mean takes every value into account equally in its calculation, making it sensitive to outliers and extreme values compared to median or mode.

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

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

  1. $1255$
  2. $1205$
  3. $1250$
  4. $1225$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of n arithmetic means inserted between two numbers a and b is equal to n times the average of a and b. Here, n = 50, a = 20, and b = 30, so the sum is 50 * (20 + 30) / 2 = 50 * 25 = 1250.

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

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

  1. $30$
  2. $29$
  3. $31$
  4. $25$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total sum of all 9 numbers is 246. The sum of the first 3 numbers is 3 * 24 = 72. The sum of the remaining 6 numbers is 246 - 72 = 174. The average of the remaining numbers is 174 / 6 = 29.

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