Cost of living Index for some period is given in the following frequency distribution: | |||||||
Index | 1500 ? 1600 | 1600 ? 1700 | 1700 ? 1800 | 1800 ? 1900 | 1900 ? 2000 | 2000 ? 2100 | 2100 ? 2200 |
No. of weeks | 3 | 11 | 12 | 7 | 9 | 8 | 2 |
Find the mode and median for above data. |
Answer:
Index Number of weeks \[({{f}_{i}})\] \[c{{f}_{i}}\] 1500 ? 1600 3 3 1600 ? 1700 11 \[{{f}_{0}}\] 14 1700 ? 1800 12 \[{{f}_{1}}\] 26 1800 ? 1900 7 \[{{f}_{2}}\] 33 1900 ? 2000 9 42 2000 ? 2100 8 50 2100 ? 2200 2 52 \[\sum{{{f}_{i}}=52}\] \[n=52\] \[\frac{n}{2}=\frac{52}{2}=26\] \[\therefore \] Median class is 1700 ? 1800 Median \[=l+\frac{\frac{n}{2}-cf}{f}\times h\] \[=1700+\frac{26-14}{12}\times 100\] \[\frac{n}{2}=1700+\left( \frac{12}{12}\times 100 \right)=1800\] Maximum frequency is 12 \[\therefore \] Modal class is 1700 ? 1800 Mode \[=l+\frac{{{f}_{1}}-{{f}_{0}}}{2{{f}_{1}}-{{f}_{0}}-{{f}_{2}}}\times h\] \[=1700+\frac{12-11}{24-11-7}\times 100\] \[=1700+\frac{1}{6}\times 100\] \[=1700+16.67\] \[=1716.67\]
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