Question

Eight randomly selected light bulbs were tested to determine their lifetimes in hours . the frequency distribution was obtained . find the standard deviation

class boundaries frequency

52.5-63-5 10

63.5-74-5 13

74.5-85.5 28

85.5-96.5 15

96.5-107.5 14

A) 188.01

B) 13.71

C) 6892.69

D) 537898.29

Answer 1

Solution:

Class (1)	Frequency (f) (2)	Mid value (x) (3)	f⋅x (4)=(2)×(3)	f⋅x2=(f⋅x)×(x) (5)=(4)×(3)
52.5 - 63.5	10	58	580	33640
63.5 - 74.5	13	69	897	61893
74.5 - 85.5	28	80	2240	179200
85.5 - 96.5	15	91	1365	124215
96.5 - 107.5	14	102	1428	145656
---	---	---	---	---
	n=80	-----	∑f⋅x=6510	∑f⋅x2=544604

Answer : Option ( B ) 13.71