Tag: introduction to averages

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

In a Maths test the average score of the $10$ girls in a class is $15$ and the average score of the $15$ boys is $10$. The average score of the class in the test is 

  1. $12$
  2. $12.5$
  3. $13$
  4. $12.75$`
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total score of 10 girls is 10 * 15 = 150. The total score of 15 boys is 15 * 10 = 150. The total class score is 300 for 25 students. The average is 300 / 25 = 12.

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

Mean deviation of first $7$ natural no. about their A.M. is?

  1. $2$
  2. $\sqrt{2}$
  3. $\dfrac{12}{7}$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first 7 natural numbers are 1, 2, 3, 4, 5, 6, 7. Their arithmetic mean (A.M.) is (1+2+3+4+5+6+7)/7 = 28/7 = 4. The absolute deviations from the mean 4 are |1-4|, |2-4|, |3-4|, |4-4|, |5-4|, |6-4|, |7-4|, which are 3, 2, 1, 0, 1, 2, 3. The sum of these deviations is 3+2+1+0+1+2+3 = 12. The mean deviation is therefore 12/7.

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

The ratio of sum of n arithmetic means between two given numbers to that of single arithmetic mean between them id

  1. n : 1
  2. n$^2$ : 1

  3. 1 : 1
  4. $\sqrt{n}$ : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of n arithmetic means between a and b is n * (a+b)/2. The single arithmetic mean is (a+b)/2. The ratio is therefore n : 1.

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

If $\cfrac {a^n+b^n}{a^{n-1}+b^{n-1}}$ is the AM between a and b, then the value of n is 

  1. 0

  2. 1

  3. -1

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

The A.M. of a and b is $\dfrac{a+b}{2}$.


Therefore, $\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}$ will be the A.M. of a and b, if 

$\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}=\dfrac{a+b}{2}$

$\Rightarrow 2(a^{n+1}+b^{n+1})=(a^n+b^n)(a+b)$

$\Rightarrow 2a^{n+1}+2b^{n+1}=a^{n+1}+a^nb+b^na+b^{n+1}$

$\Rightarrow a^{n+1}+b^{n+1}=a^nb+b^na$

$\Rightarrow a^n(a-b)=b^n(a-b)$

$\Rightarrow a^n=b^n$

$\Rightarrow \dfrac{a^n}{b^n}=1$

$\Rightarrow (\dfrac{a}{b})^n=1$

$\Rightarrow (\dfrac{a}{b})^n=(\dfrac{a}{b})^0$

$\Rightarrow n=0$

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

Find the average of the following set of scores $253,124,255,534,836,375,101,443,760$

  1. $427$
  2. $413$
  3. $141$
  4. $409$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the average, sum all the given scores and divide by the total count of numbers. The sum of 253, 124, 255, 534, 836, 375, 101, 443, and 760 is 3681, and dividing by 9 yields 409.

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

The average age of $30$ girls. is $13\ yr$. The average of first $18$ girls is $15\ yr$. Find out the average age of remaining $12$ girls? 

  1. $12\ yr$
  2. $10\ yr$
  3. $16\ yr$
  4. $10.5\ yr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Multiply the total count by the overall average to find the total sum of ages, which is 30 * 13 = 390. Next, find the sum of the ages of the first 18 girls by multiplying 18 * 15 = 270. Subtracting this from the total gives 390 - 270 = 120 for the remaining 12 girls, leading to an average of 120 / 12 = 10 years.

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

A student bought $4$ books for $Rs.120$ from one book shop and $6$ books for $Rs.150$ from another. The average price (in  rupees), he paid per book was:

  1. $27$
  2. $27.50$
  3. $135$
  4. $138$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = 120 + 150 = 270. Total books = 4 + 6 = 10. Average price = 270 / 10 = 27.

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

Let $(1-2x+3x^{2})^{10}=a _{0}+a _{1}x+a _{2}x^{2}+....+a _{n}x^{n},a _{n}\neq 0$, then the arithmetic mean of $a _{0},a _{1},a _{2},....a _{n}$ is

  1. $\dfrac{1024}{11}$
  2. $\dfrac{512}{7}$
  3. $\dfrac{512}{11}$
  4. $\dfrac{1024}{21}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The arithmetic mean of coefficients a_0, a_1, ..., a_n is the sum of coefficients divided by the number of terms, which is (1/21) * sum. By substituting x = 1 and x = -1 into the polynomial expansion, we find the sum of all coefficients and the alternating sum, allowing us to find the total sum of coefficients and compute the mean as 1024/21.

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

If $a,b,c,d,e,f$ are $A.M.s$ between $2$ and $12$ then $a+b+c+d+e+f$ is equal to

  1. $14$
  2. $42$
  3. $84$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When n arithmetic means are inserted between two numbers p and q, their sum is equal to n times the single arithmetic mean of the two numbers, or n * (p + q) / 2. Here there are 6 means between 2 and 12, so the sum is 6 * (2 + 12) / 2 = 6 * 7 = 42.

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

The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increases by 0.15 m. What is the average height of the 5 boys who leave?

  1. 0.8 m

  2. 0.9 m

  3. 0.95 m

  4. 1.05 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial total height = 25 * 1.4 = 35. New total height = 20 * 1.55 = 31. Total height of 5 boys = 35 - 31 = 4. Average = 4 / 5 = 0.8.