Multiple choice

The median value of the following data is $49.23$ and the following table represents the percentage of marks in the second term examination and number of students acquired the respective percentage. Calculate the value of x and y. The total frequency is $100$ Percentage $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ No.of students $5$ $12$ x $26$ y $18$ $12$

  1. $x=9, y=13$
  2. $x=12, y=15$
  3. $x=9, y=18$
  4. $x=18, y=19$
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C Correct answer
Explanation

The total frequency is 100, so 5 + 12 + x + 26 + y + 18 + 12 = 100, which simplifies to x + y = 27. Using the median formula for grouped data with median 49.23 (which falls in the 40-50 class), one can solve for x and y; x=9 and y=18 satisfy both the total sum and the median calculation.

AI explanation

To find the missing frequencies, we use the given total frequency and the median formula. The sum of all frequencies is 5 plus 12 plus x plus 26 plus y plus 18 plus 12, which simplifies to 73 plus x plus y; setting this equal to the total of 100 gives x plus y equals 27. Using the median formula for grouped data, we set 49.23 equal to 40 plus 10 times the quantity of 50 minus 17 minus x, all divided by 26. Solving this yields x equals 9, and substituting this into our first equation gives y equals 18.

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