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  • Find the mean age of 100 residents of a town from the following data : Age equal and above (in years) 0 10 20 30 40 50 60 70 Number of Persons 100 90 75 50 25 15 5 0

Find the mean age of 100 residents of a town from the following data :

Age equal and above (in years) 0 10 20 30 40 50 60 70
Number of Persons 100 90 75 50 25 15 5 0


 

Answers (1)

Answer. [31]

Solution. Here we calculate mean by following the given steps:

  1. Find the mid point of each interval.
  2. Multiply the frequency of each interval by its mid point.
  3. Get the sum of all the frequencies (f) and sum of all the (fx)
  4. Now divide sum of (fx) by sum of (f)
     
    Marks xi fi
    0-10 5 100-90 =10 50
    10-20 15 90-75 = 15 225
    20-30 25 75-50 = 25 625
    30-40 35 50-25 =25 875
    40-50 45 25-15 =10 450
    50-60 55 15-5 = 10 550
    60-70 65 5-0 = 5 325
        \sum f_{i}= 100 \sum f_{i}x_{i}= 3100

    mean\left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{\sum f_{i}}= \frac{3100}{100}= 31

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