Multiple choice

Class 0-20 20-40 40-60 60-80 80-100 Frequency 19 $f_1$ 32 $f_2$ 19 Total 120 Mean of the above frequency table is given as $50$. Find $f_1$ and $f_2$.

  1. $28$ and $22$
  2. $25$ and $25$
  3. $24$ and $26$
  4. $20$ and $30$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total frequency = 19 + f1 + 32 + f2 + 19 = 120, so f1 + f2 = 50. Mean = sum(fi*xi)/120 = 50. Midpoints are 10, 30, 50, 70, 90. (19*10 + f1*30 + 32*50 + f2*70 + 19*90) / 120 = 50. 190 + 30f1 + 1600 + 70f2 + 1710 = 6000. 30f1 + 70f2 = 2500, or 3f1 + 7f2 = 250. Substituting f1 = 50 - f2: 3(50-f2) + 7f2 = 250 => 150 + 4f2 = 250 => 4f2 = 100 => f2 = 25. Then f1 = 25.

Keep practicing — related questions