Question

if each observation of data is divided by 6 then the arithmetic means

Answer 1

Answer:

arithmetic mean also ÷ with 6

Answer 2

The arithmetic mean is also divided by 6

Step-by-step explanation:

Let $x_1,x_2,x_3,............................x_n$ are the n observations

Now as we know that the mean is given by

$\bar {x}= \dfrac{\text {Sum of observations}}{\text {Number of observations}}$  

Therefore we have

$\bar {x}=\dfrac{x_1+x_2+x_3+..........+x_n}{n}$

Now all observations are divided by 6

New observations becomes  $\dfrac{x_1}{6} ,\dfrac{x_2}{6} ,\dfrac{x_3}{6}........, \dfrac{x_n}{6}$

Therefore the new mean

$\bar{x}_{new}= \dfrac{\dfrac{x_1}{6} +\dfrac{x_2}{6} +\dfrac{x_3}{6}+........+\dfrac{x_n}{6}}{n} = \dfrac{1}{6} (\dfrac{x_1+x_2+x_3+..........+x_n}{n})= \dfrac{1}{6}\bar {x}$

Hence, the arithmetic mean is also divided by 6

#Learn more

Mean of n no. is x. If each observation is multiplied by 4,what will be the new mean

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