Answer to Question #86560 in Statistics and Probability for Anand

Question

The life of the bulbs produced by two companies A and B are given below:
Length Company A Company B
of life (no.of (no.of (in hours) bulbs) bulbs)
500-700 5 4
700-900 11 30
900-1100 26 12
1100-1300 10 8
1300-1500 8 6
Total 60 60
which company’s bulbs are more consistent from the point of view of length of life?
Give reasons for your answer.

Answer 1

I'm going to use some calculations aid. We can see that the average life of Company A bulbs is approx. 1016, while for Company B bulbs it is 940 hours.

Besides, the variance of the Company A list of values is smaller, which indicates also that the observed life span is more consistent (i.e. predictable) than that of Company B bulbs.

In[1]:= A={5,11,26,10,8}
Out[1]= {5,11,26,10,8}
In[2]:= B = {4,30,12,8,6}
Out[2]= {4,30,12,8,6}
In[3]:= L = {600,800,1000,1200,1400} (* average hours in each life span category *)
Out[3]= {600,800,1000,1200,1400}
In[15]:= N[Total[A*L]/Total[A]]
Out[15]= 1016.67
In[16]:= N[Total[B*L]/Total[B]]
Out[16]= 940.
In[18]:= N[Variance[A]]
Out[18]= 66.5
In[19]:= N[Variance[B]]
Out[19]= 110.