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  • The arithmetic mean of the following frequency distribution is 53. Find the value of k. Class 0-20 20-40

The arithmetic mean of the following frequency distribution is 53. Find the value of k.

Class 0-20 20-40 40-60 60-80 80-100
Frequency 12 15 32 k 13
 

 

 
 
 
 
 

Answers (1)

Class xi fi fixi
0-20 10 12 120
20-40 30 15 450
40-60 50 32 1600
60-80 70 k 70k
80-100 90 13 1170
  Total \Sigmafi= 72 + k

\Sigmafixi= 3340 +70k

\therefore    Mean \bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i}

\Rightarrow 53 = \frac{3340 + 70k}{72 + k}

\Rightarrow 3340 + 70k = 53({72 + k})

\Rightarrow 17k = 476

\Rightarrow k = \frac{476}{17}

\Rightarrow k = 28

Posted by

Safeer PP

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