The given table shows the number of people in different age groups. Find the mean age of the given number of people.

Question

The given table shows the number of people in different age groups. Find the mean age of the given number of people.

1. A. 54.2 years
2. B. 38.6 years
3. C. 32.4 years
4. D. 43.2 years (Correct answer)

Correct Answer

Option D — 43.2 years

Detailed Solution & Explanation

The correct answer is 43.2 years.

Key Points

• Take the midpoint of each class as its representative value:
  • 27, 32, 37, 42, 47, 52, 57 against frequencies 10, 12, 8, 5, 15, 10, 15
• Compute Σfx:
  • (27×10) + (32×12) + (37×8) + (42×5) + (47×15) + (52×10) + (57×15)
  • = 270 + 384 + 296 + 210 + 705 + 520 + 855 = 3240
• Σf = 75, so mean = 3240 / 75 = 43.2 years.

Additional Information

• The midpoint of a class is (lower limit + upper limit)/2, and using it assumes the values are spread evenly within each class — the standard assumption for grouped data.
• The step-deviation method shortens the arithmetic: pick an assumed mean A and class width h, then mean = A + h × (Σfu / Σf) where u = (x − A)/h.
• Note the distribution is bimodal in the tail — the 45-49 and 55-59 classes are the largest — which pulls the mean above the middle class.
• For grouped data: mode = l + h(f₁ − f₀)/(2f₁ − f₀ − f₂) and median = l + h(n/2 − cf)/f, both worth keeping alongside the mean.