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
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