Question : The frequency distribution data is given below. If the average age is 17 years, the value of m is:
Age (in years): 8, 20, 26, 29
Number of people: 3, 2, m, 1
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution :
Using frequency distribution table:
Given: The average age = 17 years
According to the question,
$\frac{8 × 3+20×2+26×m+29×1}{3+2+m+1} = 17$
⇒ $\frac{24+40+26m+29}{6+m} = 17$
⇒ $93+26m = 102+17m$
⇒ $9m=9$
$\therefore m=1$
Hence, the correct answer is 1.
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