Question

Find the mean form the following data: Find the mean form the following data No. of Students Less than 10 5 Less than 20 20 Less than 30 45 Less than 40 70 Less than 50 80 Less than 60 88 Less than 70 98 Less than 80 100

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Solution

Converting less than cumulative frequency distribution into a simple frequency distribution Marks No. of students (c.f) Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 5 20 45 70 80 88 98 100 Class Interval (Marks) Mid-Values (m) Students (f) fm 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 5 15 25 35 45 55 65 75 0-5=5 20-5=15 45-20=25 70-45=25 80-70=10 88-80=8 98-88=10 100-98=2 25 225 625 875 450 440 650 150 Σf=100 Σfm= 3440 Calculating mean from the above data by using direct method: $\overline{)\mathit{X}}=\frac{\Sigma fm}{\Sigma f}\phantom{\rule{0ex}{0ex}}or,\overline{)X}=\frac{3440}{100}\phantom{\rule{0ex}{0ex}}⇒\overline{)X}=34.4\mathrm{marks}$ Hence, the mean of the above data is 34.4 marks.

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