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Measures of Dispersion
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.
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In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.
If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?
The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.
Calculate the mean deviation about mean and standard deviation for the following distribution:
|
Classes |
Frequencies |
|
20–40 |
3 |
|
40–80 |
6 |
|
80–100 |
20 |
|
100–120 |
12 |
|
120–140 |
9 |
|
50 |
A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment
Define dispersion.
How many methods are there to calculate dipersion?
Define range.
Define quartile deviation.
How is coefficient of quartile deviation calculated?
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