Multiple choice

The following distribution gives the state-wise teacher student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures. No. of students per teacher No. of state/ U.T. 15-20 3 20-25 8 25-30 9 30-35 10 35-40 3 40-45 0 45-50 0 50-55 2

  1. $Mode=31.7, Mean=28.2$
  2. $Mode=33.6, Mean=25.3$
  3. $Mode=35.7, Mean=26.3$
  4. $Mode=30.6, Mean=29.2$
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D Correct answer
Explanation

Calculating the mean: Midpoints are 17.5, 22.5, 27.5, 32.5, 37.5, 52.5. Frequencies are 3, 8, 9, 10, 3, 2. Sum of f*x = 52.5 + 180 + 247.5 + 325 + 112.5 + 105 = 1022.5. Total frequency = 35. Mean = 1022.5 / 35 = 29.21. Mode is in the 30-35 class: 30 + ((10-9)/(2*(10)-9-3)) * 5 = 30 + (1/8)*5 = 30.625.

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