Question

1. Find the missing frequencies (f1, f2 and f3) in the following frequency distribution
when it is given that f2 : f3 = 4: 3 and mean = 50.
Class Interval
20-40
40-60
60-80
frequency
0-20
17
80-100
19
total
120​

Answer 1

Answer:

Class- Interval    Mid value(V) Frequency()      V F

0-20                10                        17                            170

20-40              30                       f 1                             30 f 1

40-60              50                       f 2                            50 f 2

60-80              70                       f 3                            70 f 3

90-100             90                      19                             1710

SUM(F)=120  SUM(VF)=Mean=50

1. 17+f 1+f 2+f 3+19= 120

 → f 1+f 2+f 3

    = 120 - 36=84

→ f 2 : f 3 = 4 : 3

So,Let, f 2 and f 3 = 4 k and 3 k

→f 1 + 4 k + 3 k= 84

→→f 1 + 7 k= 84------(1)

2. 170 + 30 f 1 + 50 f 2 + 70 f 3 + 1710 = 50×120

→170 + 30 f 1 + 50 × 4 k + 70 × 3 k + 1710= 6000

→170 + 30 f 1 + 200 k + 210 k + 1710= 6000

→30 f 1 + 410 k= 4120

→ 3 f 1 + 41 k = 412   ----(2)

→f 1 + 7 k= 84------(1)

=3 × equation(1) - equation (2)

⇒21 k - 41 k = 252- 412

⇒- 20 k = - 160

⇒k=8

Substituting the value of k in equation (2)

→ f 1 +56=84

→ f 1 = 84-56

→  f 1= 28

→f 2 = 4 × 8= 32

→f 3 = 3 × 8 = 24

MARK AS "BRAINIEST" ANSWER.

Step-by-step explanation: