Question: Compute quartile deviation and its coefficient from the following data: Mid value (yrs.) 62.5 67.5 72.5 77.5 82.5 87.5 Frequency 7 5 8 4 3 3 Solution: Given, Arranging the given data in cumulative frequency (c.f.) table: Class Frequency (f) c.f. 62.5 (60-65) 7 7 67.5 (65-70) 5 12 72.5 (70-75) 8 20 77.5 (75-80) 4 24 82.5 (8…

Question: Find the inter-quartile range and coefficient of quartile deviation from the following data: Weight (Kg) 10-20 10-30 10-40 10-50 10-60 10-70 No. of men 12 31 36 46 55 61 Solution: Given, Arranging the given data in cumulative frequency (c.f.) table: Marks (x) No. (f) c.f. 10-20 (10-20) 12 12 10-30 (20-30) 19 31 10…

Question: Find the quartile deviation from the following data: Marks <5 <10 <15 <20 <25 <30 Frequency (f) 2 4 7 13 27 40 Solution: Given, Arranging the given data in cumulative frequency (c.f.) table: Marks (x) No. (f) c.f. <5 (0-5) 2 2 <10 (5-10) 2 4 <15 (10-15) 3 7 <20 (15-20) 6 13 <25 (20-25) 14 2…

Question: Calculate the quartile deviation and its coefficient from the data given. Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of students 4 3 7 22 7 2 Solution: Given, Arranging the given data in cumulative frequency (c.f.) table: Marks (x) No. (f) c.f. 0-10 4 4 10-20 3 7 20-30 7 14 30-40 22 36 40-50 7 43 50-60 2 45 N = …

Question: Calculate the quartile deviation from the data given. Age (in years) 10-20 20-30 30-40 40-50 50-60 No. of workers 2 6 22 13 7 Solution: Given, Arranging the given data in cumulative frequency (c.f.) table: Age (x) No. (f) c.f. 10-20 2 2 20-30 6 8 30-40 22 30 40-50 13 43 50-60 7 50 N = 50 Now , $Q_1 \; …

Question: The third quartile of a data is 15. If the coefficient of quartile deviation is 1/4, find the first quartile and the inter-quartile range of the data. Solution: Given, Third quartile ($Q_3$) = 15 Coefficient of Quartile Deviation = $\frac{1}{4}$ To find: First Quartile = ? And Inter-quartile range= ? We know, Coefficient o…

Question: The third quartile and inter-quartile range of a data are 58 and 28 respectively. Find the coefficient of the quartile deviation. Solution: Given, Third quartile ($Q_3$) = 58 Inter-quartile range = 28 To find: Coefficient of Quartile Deviation = ? We know, Inter-quartile range = $Q_3 - Q_1$ $or, 28 = 58 - Q_1$ $or, Q_1 = 5…

Question: In a data, the quartile deviation and its coefficient are 15 and 3/7 respectively. Find the first quartile. Solution: Given, Quartile Deviation (Q.D.) = 15 Coefficient of Q.D. = $\frac{3}{7}$ To find: First Quartile ($Q_1$) = ? We know, $Q.D. = \dfrac{Q_3 - Q_1}{2}$ $or, 15 = \dfrac{Q_3 - Q_1}{2}$ $or, 15 × 2 = Q_3 - Q_1$ …

Question: In a day, quartile deviation and the first quartile are 20 and 35 respectively. Find its third quartile and the coefficient of quartile deviation. Solution: Given, Quartile Deviation (Q.D.) = 20 First Quartile ($Q_1$) = 35 To find: Third Quartile ($Q_3$) = ? We know, $Q.D. = \dfrac{Q_3 - Q_1}{2}$ $or, 20 = \dfrac{Q_3 - 35}…

Question: In a data, the first quartile is 35 and the third quartile is 75. Find the quartile deviation and its coefficient. Solution: Given, First quartile ($Q_1$) = 35 Third quartile ($Q_3$) = 75 Now, Quartile Deviation (Q.D.) = $\dfrac{Q_3 - Q_1}{2}$ $= \dfrac{75-35}{2}$ $= \dfrac{40}{2}$ $= 20 And, Coefficient of Q.D. = $\dfrac{…