Multiple choice

The percentage of marks obtained by the students in a class of $50$ are given below. Find the mean for the following data. Marks$(\%)$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$ Number of students $6$ $12$ $14$ $8$ $6$ $4$

  1. $64.6\%$
  2. $65.6\%$
  3. $66.6\%$
  4. $67.6\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Midpoints: 45, 55, 65, 75, 85, 95. Frequencies: 6, 12, 14, 8, 6, 4. Mean = (45*6 + 55*12 + 65*14 + 75*8 + 85*6 + 95*4) / 50 = (270 + 660 + 910 + 600 + 510 + 380) / 50 = 3330 / 50 = 66.6.

AI explanation

Using the assumed mean method, we find the class marks of the given intervals and set the assumed mean a to 65. The sum of the products of deviations and frequencies is (negative 4 times 6) plus (negative 2 times 12) plus (0 times 14) plus (2 times 8) plus (4 times 6) plus (6 times 4), which equals 8. The total number of students is 6 plus 12 plus 14 plus 8 plus 6 plus 4, which equals 50. The mean is 65 plus (8 divided by 50) times 10, which equals 65 plus 1.6, resulting in 66.6 percent.

Keep practicing — related questions