Question

Question 1 (a): A class consists of 100 students with boys and girls’ ratios as 4:6. Find the average weight of the class if the average weight of boys and girls is 10 and 15
respectively. Also find the combined mean if the ratio of no of boys and girls is reversed.

Question 1 (b): The rice production (in Kg) of 10 acres is given as: 1120, 1240, 1320, 1040, 1080, 1720, 1600, 1470, 1750, and 1885. Find the quartile deviation and coefficient of quartile deviation.

Answer 1

n1= number of boys

n2= number of girls

n1 : n2 = 4 : 6

Class consist of 100 students, i.e = n1+n2 = 100

4 x + 6 x = 100

10 x = 100

x = 10

Number of boys = 4 x = 4*10 = 40

Number of girls = 6*10 = 60

Average weight of boys = 10

Average weight of girls = 15

Total weight of boys = 40*10 = 400

Total weight of girls = 60 * 15 = 900

Average weight of the class = (Total weight of boys + Total weight of girls ) / Total number of students

= (400+900) / 100

= 13

Combined mean if the ratio of no of boys and girls is reversed,i.e . 6:4

Number of boys =n1= 60

Number of girls =n2= 40

Average weight of boys == 10

Average weight of girls =2= 15

Combined mean =

  

=

b) 1120, 1240, 1320, 1040, 1080, 1720, 1600, 1470, 1750, and 1885

Increasing order

1040,1080,1120,1240,1320,1470,1600,1720,1750,1885

n = 10

Q1 =

Q1 =

= 2.75^th observation

= 2^nd observation + 0.75( 3^rdobservation - 2^nd observation)

= 1080 + 0.75(1120-1080)

= 1080+30

Q1 = 1110

Q3 =

=

=

= 8.25^th observation

= 8^th observation + 0.25 (9^th observation - 8^th observation)

= 1720 + 0.25 (1750-1720)

= 1720 + 7.5

Q3 = 1727.5

Quartile deviation =

=

= 308.75

Coefficient of Quartile deviation =

=

= 0.2176