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  • If the frequencies of first four numbers out of 1, 2, 4, 6, 8 are 2, 3, 3 , 2 respectively, then the frequency of 8

If the frequencies of first four numbers out of 1, 2, 4, 6, 8 are 2, 3, 3 , 2 respectively, then the frequency of 8 if their AM is 5, is

Option: 1

4


Option: 2

5


Option: 3

6


Option: 4

None of these 


Answers (1)

best_answer

As we have learned

Properties of ARITHMETIC Mean -

Sum of deviation from a.m is zero.

\left ( x_{1}-\bar{x} \right )+\left ( x_{2}-\bar{x} \right )+\cdots \left ( x_{n}-\bar{x} \right )= 0

-

 

ARITHMETIC Mean -

In case of discrete frquency distribution:

If the observations x1, x2, ......xn occur with frequencies f1, f2, ....fn then

\bar{x} = \frac{f_{1}x_{1}+f_{2}x_{2}+\cdots f_{n}x_{n}}{f_{1}+f_{2}+f_{3}+\cdots f_{n}}

\dpi{100} = \frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}= \frac{1}{N}\sum_{i=1}^{n}f_{i}x_{i}

- wherein

where

N= \sum_{i=1}^{n}f_{i}

 

 

Here mean A = 5

                Let the frequency of 8 be x. Then by the formula

                        A=\frac{\sum xf}{\sum f}

                        5=\frac{1.2+2.3+4.3+6.2+8x}{2+3+3+2}=\frac{32+8x}{10+x}

                or    18 = 3x; \ x = 6.

Posted by

Ritika Jonwal

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