Question

10) frequency distribution of the life times of 400 TV, picture tubes
tested in a tube company is given below. Find the average life of tube by a
step deviation method
Expenditure (in Rs)
Frequency
300-399
400 499
46
500-599
58
600-699
76
700-799
68
800-899
62
48
22
1100 1199
6​

Answer 1

Answer:

Here, the class- intervals are formed by exclusive method. If we make the series an inclusive one the mid-values remain same. So, there is no need to convert the series into an inclusive form.

Let the assumed mean be A= 749.5 and h= 100.

Calculation of Mean

Life time (in hrs): Frequency

f

i

Mid-Values

x

i

d

i

=x

i

−A=x

i

−749.5 u

i

=

h

x

i

−A

u

i

=

100

x

i

−749.5

f

i

u

i

300-399 14 349.5 -400 -4 -56

400-499 46 449.5 -300 -3 -138

500-599 58 549.5 -200 -2 -116

600-699 76 649.5 -100 -1 -76

700-799 68 749.5 0 0 0

800-899 62 849.5 100 1 62

900-999 48 949.5 200 2 96

1000-1099 22 1049.5 300 3 66

1100-1199 6 1149.5 400 4 24

N=∑f

i

=400 ∑f

i

u

i

=-138

We have,

N= 400, A= 749.5, h= 100 and ∑f

i

u

i

=−138

∴

X

=A+h[

N

1

∑f

i

u

i

]

⇒

X

=749.5+100(

400

−138

)=749.5−34.5=715.

Hence, the average life time of a tube is 715 hours.