question_answer

The mean of the following distribution is 18. Find the frequency f of the class 19 ? 21.
Class	11 ? 13		13 ? 15		15 ? 17	17 ? 19	19 ? 21		21 ? 23		23 ? 25
Frequency	3		6		9	13	f		5		4
OR
The following distribution gives the daily income of 50 workers of a factory:
Daily Income (in Rs.)		100 ? 120		120 ? 140		140 ? 160		160 ? 180		180 ? 200
Number of workers		12		14		8		6		10
Convert the distribution above to a less than type cumulative frequency distribution and draw it?s give.

Answer:

C.I.	Mid value \[{{x}_{i}}\]	\[{{f}_{i}}\]		\[{{f}_{i}}{{x}_{i}}\]
11 ? 13	12	3		36
13 ? 15	14	6		84
15 ? 17	16	9		144
17 ? 19	18	13		234
19 ? 21	20	f		20f
21 ? 23	22	5		110
23 ? 25	24	4		96
Total		\[\sum{{{f}_{i}}=40+f}\]		\[\sum{{{f}_{i}}{{x}_{i}}=704+20f}\]
Now,                 Mean = 18                    (Given)
\[\Rightarrow \]               \[\frac{\sum{{{f}_{i}}{{x}_{i}}}}{\sum{{{f}_{i}}}}=18\]
\[\therefore \]                  \[\frac{704+20f}{40+f}=18\]
\[\Rightarrow \]               \[704+20f=18(40+f)\]
\[\Rightarrow \]               \[704+20f=720+18f\]
\[\Rightarrow \]               \[20f-18f=720-704\]
\[\Rightarrow \]                          \[2f=16\]
\[\Rightarrow \]                            \[f=8\]
OR
Less than type cumulative frequency distribution:
Daily Income			No. of workers
Less than 120			12
Less than 140			26
Less than 160			34
Less than 180			40
Less than 200			50