For helping poor girls of their class, students saved pocket money as shown in the following table: | |||||
Money saved (in Rs.) | 5 ? 7 | 7 ? 9 | 9 ? 11 | 11 ? 13 | 13 ? 15 |
Number of students | 6 | 3 | 9 | 5 | 7 |
Find mean and median for this data. |
Answer:
Money saved (in Rs.) No, of Students \[({{f}_{i}})\] \[{{X}_{i}}\] \[{{d}_{i}}=\frac{{{X}_{i}}-10}{2}\] \[{{f}_{i}}{{d}_{i}}\] \[c.f.\] 5 ? 7 6 6 \[2\] \[-12\] 6 7 ? 9 3 8 \[1\] \[-3\] 9 9 ? 11 9 \[a=10\] 0 0 18 11 ? 13 5 12 1 5 23 13 ? 15 7 14 2 14 30 \[\sum{{{f}_{i}}=30}\] \[\sum{{{f}_{i}}{{d}_{i}}=4}\] (i) Mean \[=a+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h\] \[=10+\frac{4}{30}\times 2=10+0.27\] \[=Rs.\,10.27\] (ii) \[N=\sum{{{f}_{i}}=30}\] \[\frac{N}{2}=\frac{30}{2}=15,\] \[\therefore \] Median class is 9 ? 11. Median \[=l+\frac{\frac{N}{2}-F}{f}\times h\] \[=9+\frac{15-9}{9}\times 2=9+\frac{6}{9}\times 2\] \[=9+1.33=Rs.\,\,10.33\]
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