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Question

Find the Quartile Deviation for the following set of data:
$$490, 540, 590, 600, 620, 650, 680, 770, 830, 840, 890, 900$$


A
12
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B
122.5
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C
13
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D
12.6
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Solution

The correct option is C $$122.5$$
$$490, 540, 590, 600, 620, 650, 680, 770, 830, 840, 890, 900$$
$$Q_d=\dfrac{Q_3-Q_1}{2}$$
$$Q_d\rightarrow$$ Quality deviation
$$Q_1\rightarrow 25^{th}$$ perentile
$$Q_3\rightarrow 75^{th}$$ perentile
$$Q_1=\left(\dfrac{n+1}{4}\right)$$th term
$$=\dfrac{13}{4}$$th term
$$=3.25$$th term
$$=3^{rd}$$ term$$+0.25\times (4^{th}$$ term$$-3^{rd}$$ term$$)$$
$$=590+0.25\times (600-590)$$
$$=590+0.25\times 10$$
$$Q_1=592.5$$
$$Q_3=\dfrac{3(n+1)}{4}$$th term
$$=\dfrac{3}{4}\times 13=9.75^{th}$$ term
$$=9^{th}$$ term$$+0.75\times (10^{th}$$ term$$-9^{th}$$ term$$)$$
$$=830+0.75\times (840-830)$$
$$=830+7.5$$
$$Q_3=837.5$$
$$Q_d=\dfrac{Q_3-Q_1}{2}$$
$$=\dfrac{837.5-592.5}{2}=\dfrac{245}{2}=122.5$$.

1154371_697678_ans_a1e9eaf083d04f19819867528ef1373c.jpg

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