Question

Following are observation showing the age of employee working in a industry , find inter - quartile deviation , quartile deviation and coefficients of quartile .
( class 11th , economics , isc book) ​

Answer 1

Answer:

Inter quartile deviation = 19.22

Quartile deviation = 9.16

Coefficient of quartile = 0.319

Table:

$\begin{array}{|c|c|c|}\cline{1-3}&&\\& &\\\bf Age(C.I.)& \bf frequency & \bf Cumulative \:frequency(c.f)\\& &\\\cline{1-3}&&\\0-10&8&8\\&&\\10-20&16&24\\&&\\20-30&22&46\\&&\\30-40&30&76\\&&\\40-50&24&100\\&&\\\cline{1-3}&&\\&\sum f=100&\\&&\\\cline{1-3}\end{array}$

app user refer to attachment

cd = 10-0

cd = 10

$\sf \: Inter \: quartile \: deviation \: = Q_3 - Q_1 \\ \\ \sf \: Quartile \: deviation \: = \frac{ Q_3 - Q_1}{2} \\ \\ \sf \:Coefficient \: of \: quartile \: = \frac{Q_3 - Q_1}{Q_3 + Q_1} \\ \\ \sf \: Q_1 = \bigg(\dfrac{ N}{4} \bigg) ^{th} item \\ \\ \implies \: \bigg(\dfrac{ 100}{4} \bigg) ^{th} item \\ \\ \implies \: {25}^{th} item \\ \\ \sf \: Q_1 = L_1 + \frac{\bigg(\dfrac{ N}{4} \bigg) ^{th} - cf}{f} \times cd \\ \\ \implies \:20 + \frac{25 - 24}{22} \times 10 \\ \\ \implies \:20 + \frac{10}{22} \\ \\ \implies \: \frac{440 + 10}{22} \\ \\ \implies \:20.45\\ \\ \sf \: Q_3 = 3 \bigg(\dfrac{ N}{4} \bigg) ^{th} item \\ \\\implies \:3 \bigg(\dfrac{ 100}{4} \bigg) ^{th} item \\ \\\implies {75}^{th} item \\ \\ \sf \: Q_3 = L_1 + \frac{3\bigg(\dfrac{ N}{4} \bigg) ^{th} - cf}{f} \times cd$

$\implies\sf \:30 + \frac{75 - 46}{30 } \times 10 \\ \\ \implies \: 30 + \frac{290}{30} \\ \\ \implies \: \frac{900 + 290}{30} \\ \\ \implies \:39.67$

$\sf \: Inter \: quartile \: deviation \: = Q_3 - Q_1 \\ \\ \implies 39.67 - 20.45\\ \\ \implies19.22$

$\sf \: Quartile \: deviation \: = \frac{ Q_3 - Q_1}{2} \\ \\ \implies \: \frac{39.67 - 20.45}{2} \\ \\ \implies \: \frac{19.22}{2} \\ \\ \implies \:9.61$

$\sf \: coefficien \: of \: Quartile \: deviation \: = \frac{ Q_3 - Q_1}{Q_3 +Q_1 } \\ \\ \implies \frac{39.67 - 20.45}{39.67 + 20.45} \\ \\ \implies \frac{19.22}{60.12} \\ \\ \implies0.319$

Answer 2

Answer:

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