Dear Student, Class f cf 10-20 10 10 20-30 20 30 Q1 30-40 15 45 Q3 40-50 5 50 N=50 Q1= Size of N4th item =504th item =12 5th itemThus C I for Q1 is 20-30 Q1=l1+N4-cff×i = 20+12 5-1020×10 = 20+2 52 =21 25 Q3= Size of 3N4th item =3504th item =37 5th itemThus C I for Q1 is 30-40 Q3=l1+3N4-cff×i = 30+37 5-3015×10 = 35+5 =40 IQR =Q3-Q12 =40-21 252=9 375 Regards

Calculate IQR please

Dear Student,

Class	f	cf
10-20	10	10
20-30	20	30	$Q_{1}$
30-40	15	45	$Q_{3}$
40-50	5	50
	N=50

Q_{1} = S i z e o f {(\frac{N}{4})}^{t h} i t e m = {(\frac{50}{4})}^{t h} i t e m = 12 . 5^{t h} i t e m T h u s C . I . f o r Q_{1} i s 20 - 30

Q_{1} = l_{1} + \frac{\frac{N}{4} - c f}{f} \times i = 20 + \frac{12.5 - 10}{20} \times 10 = 20 + \frac{2.5}{2} = 21.25

Q_{3} = S i z e o f 3 {(\frac{N}{4})}^{t h} i t e m = 3 {(\frac{50}{4})}^{t h} i t e m = 37 . 5^{t h} i t e m T h u s C . I . f o r Q_{1} i s 30 - 40

Q_{3} = l_{1} + \frac{3 (\frac{N}{4}) - c f}{f} \times i = 30 + \frac{37.5 - 30}{15} \times 10 = 35 + 5 = 40

IQR =

\frac{Q_{3} - Q_{1}}{2} = \frac{40 - 21.25}{2} = 9.375

Regards

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