The range, quartile deviation mean deviation and standard deviati… - Vidyadip

Question

The range, quartile deviation mean deviation and standard deviation for a variable $x$ are $10, 2, 3$ and $5$ respectively. Ify $= 5x + 3$ ﬁnd the range, quartile deviation, mean deviation and standard deviation for the variable $y.$

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Answer

Here, For variable $x$, Range $R_{x}=10$, Quartile deviation $Q_{d x}=2$, Mean deviation $M D_{x}=3$, standard deviation $s_{x}=5$.
Now, $y=5 x+3$. Using the results discussed earlier, the measures of dispersion for the variable $y$ are obtained as follows.
Range $\quad R_{y}=|5| \cdot R_{x}=5(10)=50$ Quartile deviation $Q_{d y}=|5| \cdot Q_{d x}=5(2)=10$
Mean deviation $\quad M D_{y}=|5| \cdot M D_{x}=5(3)=15$
standard deviation $s_{y}=|5| \cdot s_{x}=5(5)=25$

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