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If a and b are two positive numbers, then prove that `A.M. ge G.M. ge H.M. `

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For any two positive numbers a and b,prove that AMgeGM

For a set of positive quantities, Prove that A.M. ge GM ge H.M. .

For a set of an positive quantities prove that AM ge GM ge HM .

If the values of a variable are in G.P, then prove that A.M., G.M., H.M. of the values are also in G.P.

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

State the condition when A.M. = G.M. = H.M.

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A pm sqrt((A+G )(A−G )) .

If A is the A.M. and G is the G.M. of two unequal positive real numbers p and q, prove that A gt G and |G| gt (G^(2))/(A)

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4

If a is A.M. of two positive numbers b and c and two G.M's between b and c are G_(1) and G_(2) , prove that G_(1)^(3) + G_(2)^(3) = 2abc .

CALCUTTA BOOK HOUSE-MEASURES OF CENTRAL TENDENCY-EXERCISE
  1. If a and b are two positive numbers, then prove that A.M. ge G.M. ge H...

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  2. How arithmetic mean is changed when the values of the variable are add...

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  3. How AM, GM and HM of the values of a variable are changed when the val...

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  4. Find the average of first n-natural numbers.

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  5. What is the algebraic sum of the deviations of the values of a variabl...

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  6. If two positive values of a variable be x(1) and x(2) and the arithmet...

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  7. Find the average of the variable. The incomes of three friends are ...

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  8. Find the average of the variable. The diameters of five pipes are :...

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  9. Find the average of the variable. The selling prices of seven days ...

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  10. In the following table the prices of salt per quintal of secen days of...

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  11. The marks obtained by 30 students in a examination of a class are give...

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  12. The frequency distribution of the family members of 65 families are gi...

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  13. The weights (in Kg) and their frequency distribution of 100 students a...

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  14. The frequency distribution of the number of accidents in 30 consecutiv...

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  15. The frequency distribution of the diameters (in mm) of 80 pipes are gi...

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  16. Find the average of the numbers from the given frequency distribution ...

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  17. The frequency distributions of the quantity (in quintals) of producing...

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  18. The frequency distribution of the monthly incomes (in rupees) of the w...

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  19. The average of weights (in kg) and the number of students of a school ...

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  20. The arithmetic mean of the marks obtained in 8 different subjects in a...

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  21. The average of the collective ages of 4 classes in a school is 8.5 yea...

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