10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer
    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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