Question

Harmonic mean of the reciprocal of even numbers from 2 to 200 is

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{6},\;.\;.\;.\dfrac{1}{200}}$

$\underline{\textbf{To find:}}$

$\textsf{Harmonic mean of}\;\mathsf{\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{6},\;.\;.\;.\dfrac{1}{200}}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\mathsf{Let\;x_1,x_2,x_3\;.\;.\;.\;.x_n\;be\;the\;given\;n\;values}$

$\mathsf{Then\;its\;Harmonic\;mean=\dfrac{n}{\dfrac{1}{x_1}+\dfrac{1}{x_2}+\;.\;.\;.+\dfrac{1}{x_n}}}$

$\underline{\mathsf{Harmonic\;mean}}$

$\mathsf{=\dfrac{n}{\dfrac{1}{x_1}+\dfrac{1}{x_2}+\;.\;.\;.+\dfrac{1}{x_n}}}$

$\mathsf{=\dfrac{100}{\dfrac{1}{1/2}+\dfrac{1}{1/4}+\;.\;.\;.+\dfrac{1}{1/200}}}$

$\mathsf{=\dfrac{100}{2+4+\;.\;.\;.+200}}$

$\mathsf{=\dfrac{100}{2(1+2+3+\;.\;.\;.+100)}}$

$\mathsf{=\dfrac{100}{2{\times}\dfrac{100{\times}101}{2}}}}$

$\mathsf{=\dfrac{100}{100{\times}101}}$

$\mathsf{=\dfrac{1}{101}}$

$\mathsf{=0.01}$

$\underline{\textbf{Find more:}}$

The marks obtained by 37 students of std 8 in a Test of 10 marks are givenbelow. Find the mean of the data.. -

2, 4, 4, 8, 6, 7, 3, 8, 9, 10, 10, 8, 9, 7, 6, 5. 4, 6, 7, 8, 4, 8, 9, 7, 6, 5, 10.9, 7.9.

10. 9. 6. 9. 9. 4. 7​

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