Answer to Question #254532 in Statistics and Probability for Tege

Question

The following table gives the life time is among 400 radio tube of certain make 

Find the mean life-time of the radio tubes

Life-time(in hours)

Number of tubes

Less than 300

Less than 400

Less than 500

Less than 600

Less than 700

Less than 800

Less than 900

Less than 1000

Less than 1100

Less than 1200

20

60

116

194

265

324

374

392

400

Answer 1

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

We have,

$N= 400, A= 749.5, h= 100 \space and ∑f_i ​u_i ​=−138 ∴X =A+h[∑_1^Nf_iu_i ​] ⇒X =749.5+100(400 −138 ​)=749.5−34.5=715.$

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