To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.
|
Life (in hrs) |
No. of bulbs |
||
|
Brand A |
Brand B |
||
|
0–50 |
15 |
2 |
|
|
50–100 |
20 |
8 |
|
|
100–150 |
18 |
60 |
|
|
150–200 |
25 |
25 |
|
|
200–250 |
22 |
5 |
|
|
100 |
100 |
||
(i) Which brand gives higher life?
(ii) Which brand is more dependable?Brand A of light bulbs
|
Life |
No. of |
Mid-points |
d |
d1 |
fd' |
fd2 |
|
|
(in hrs) |
Bulbs (f) |
(m) |
(m – 125) |
|
|||
|
0–50 |
15 |
25 |
–100 |
–2 |
–30 |
60 |
|
|
50–100 |
20 |
75 |
–50 |
–1 |
–20 |
20 |
|
|
100–150 |
18 |
125 |
0 |
0 |
0 |
0 |
|
|
150–200 |
25 |
175 |
50 |
+1 |
25 |
25 |
|
|
200–250 |
22 |
250 |
100 |
2 |
44 |
88 |
|
|
N = 100 |
Σfd' = 19 |
Σfd2 =193 |
|||||
Brand B
|
Life |
No. of |
M.V. |
d |
|
fd' |
fd'2 |
|
|
(in hrs) |
Bulbs |
(m) |
d1 |
||||
|
0–50 |
2 |
25 |
–100 |
–2 |
–4 |
8 |
|
|
50–100 |
8 |
75 |
–50 |
–1 |
–8 |
8 |
|
|
100–150 |
60 |
125 |
0 |
0 |
0 |
0 |
|
|
150–200 |
25 |
175 |
+50 |
+1 |
+25 |
25 |
|
|
200–250 |
5 |
225 |
+100 |
+2 |
+10 |
20 |
|
|
N= 100 |
Σfd' =23 |
Σfd'2 = 61 |
|||||
(i) Since the average life of bulbs of Brand B (136.5) is greater than that of Brand A (134.5 hrs), therefore the bulbs of Brand B givens a higher life.
(ii) Since CV of bulbs of Brand B (27.34%) is less than that of Brand A (51.15%), therefore, the bulbs of Brand B are more dependable.
