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Examples 1 to 4

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(1) Find  the A.M., G.M.  and  H.M.  of  9 and  49.

Soln. A.M.  =  \frac{9+49}{2}=28  =  28   ;

G.M.  =  \sqrt{9 \times 49}  =  ( 3 \times 7 )  =  21   ;

H.M.  =  \frac{2 \times 9 \times 49}{9+49}  =   \frac{2 \times 9 \times 49}{56}   =   15.75

(2) Find  A.M.  of   45, 52, 58, 62  &  53

  (ii) G.M.  of   24, 21, 63  &  98.

  (iii) H.M.  of   10, 15  &  20

Soln. (i) A.M.  =  \frac{45+52+58+62+53}{5}   =   \frac{270}{5}   =   54.

 (ii) G.M. = \sqrt[4]{24 \times 21 \times 63 \times 98} = \sqrt[4]{\left (2 \times 2 \times 2 \times 3 \right ) \times \left (3 \times7 \right ) \times \left (3 \times 3 \times 7 \right ) \times \left (2 \times 7\times 7 \right )} = 42

(iii) H.M.  =  \frac{3}{\frac{1}{10} + \frac{1}{15} + \frac{1}{20}}  =  \frac{3}{\frac{6+4+3}{60}} =  3 \times \frac{60}{13}  =  13.85

(3) What is the mode of  2, 5, 7, 8, 6, 4, 5, 8, 5, 2, 5     ?

Soln. Z    =    The observation which is repeated for maximum number of times    =    5

(4) Find  the mode of the following frequency distribution :

Term 0 1 2 3 4
Frequency 15 21 29 35 7

Soln. Z   =   The observation against maximum Frequency    =    3

 

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