The table below shows the salaries of 280 persons: | |
Salary (In thousand Rs.) | No. of Persons |
5 ? 10 | 49 |
10 ? 15 | 133 |
15 ? 20 | 63 |
20 ? 25 | 15 |
25 ? 30 | 6 |
30 ? 35 | 7 |
35 ? 40 | 4 |
40 ? 45 | 2 |
45 ? 50 | 1 |
Calculate the median salary of the data. |
Answer:
Salary No. of Persons Cumulative frequency (c.f.) 5 ? 10 49 182 15 ? 20 63 245 20 ? 25 15 260 25 ? 30 6 266 30 ? 35 7 273 35 ? 40 4 277 40 ? 45 2 279 45 ? 50 1 280 Total 280 \[\frac{N}{2}=\frac{280}{2}=140\] The cumulative frequency just greater than 140 is 182. \[\therefore \] Median class is 10 ? 15. \[\Rightarrow \]\[l=10,h=5,N=280,\,c.f=49\,\] and \[f=133\] Median \[=1+\left( \frac{\frac{N}{2}-c.f.}{f} \right)\times h\] \[=10+\left( \frac{140-49}{133} \right)\times 5\] \[=10+\frac{91\times 5}{133}\] \[=10+\frac{455}{133}\] \[=10+3.42\] \[=13.42\]
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