Following table shows marks (out of 100) of students in a class test: | |
Marks | No. of students |
More than or equal to 0 | 80 |
More than or equal to 10 | 77 |
More than or equal to 20 | 72 |
More than or equal to 30 | 65 |
More than or equal to 40 | 55 |
More than or equal to 50 | 43 |
More than or equal to 60 | 28 |
More than or equal to 70 | 16 |
More than or equal to 80 | 10 |
More than or equal to 90 | 8 |
More than or equal to 100 | 0 |
Draw a ?more than type? ogive. From the curve, find the median. Also, check the value of the median by actual calculation. |
Answer:
More than type C.I. No. of Students Frequency c.f. More than or equal to 0 0 ? 10 80 3 3 More than or equal to 10 10 ? 20 77 5 8 More than or equal to 20 20 ? 30 72 7 15 More than or equal to 30 30 ? 40 65 10 25 More than or equal to 40 40 ? 50 55 12 37 More than or equal to 50 50 ? 60 43 15 52 More than or equal to 60 60 ? 70 28 12 64 More than or equal to 70 70 ? 80 16 06 70 More than or equal to 80 80 ? 90 10 02 72 More than or equal to 90 90 ? 100 8 08 80 More than or equal to 100 100 ? 110 0 00 Median will be 52 Median by actual calculation: \[N=80\] (even) \[=\frac{80}{2}\] \[=40\] So modal class will be \[5060\] \[l=50,\,h=10,\,f=15,\] \[c.f.=37\], Median \[=l+\left[ h\times \frac{\left( \frac{N}{2}-c.f. \right)}{f} \right]\] \[=50+\left[ 10\frac{(40-37)}{15} \right]\] \[=50+10\times \frac{3}{15}\] \[=50+2\] \[=52\] Hence Verified.
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