• # question_answer 30) 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.

 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