Ex.14.4 Q5 Statistics Solution - NCERT Maths Class 9

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Question

Find the mean salary of \(60\) workers of a factory from the following table:

Salary (in Rs.) Number of Workers
\(3000\) \(16\)
\(4000\) \(12\)
\(5000\) \(10\)
\(6000\) \(8\)
\(7000\) \(6\)
\(8000\) \(4\)
\(9000\) \(3\)
\(10000\) \(1\)
Total 60

Text Solution

What is known?

Salary of \(60\) workers in tabular form 

What is unknown?

Mean of the given data 

Steps:

We know that 

Mean \(=\) \(\begin{align} \frac{{\sum {{f_i}{x_i}} }}{{\sum {{f_i}} }}\end{align} \)

The value of\(\sum {{f_i}{x_i}} \)   and  \(\sum {{f_i}} \) f can be calculated as follows.

Salary \(\left(x_{i}\right)\) Number of Workers \(\left(f_{i}\right)\) \(f_{i} x_{i}\)
\(3000\) \(16\) \(16 \times 3000=48000\)
\(4000\) \(12\) \(12 \times 4000=48000\)
\(5000\) \(10\) \(10 \times 5000=50000\)
\(6000\) \(8\) \(8 \times 6000=48000\)
\(7000\) \(6\) \(6 \times 7000=42000\)
\(8000\) \(4\) \(4 \times 8000=32000\)
\(9000\) \(3\) \(3 \times 9000=27000\)
\(10000\) \(1\) \(1 \times 10000=10000\)
Total \(\sum f_{i}=60\) \(\sum f_{i} x_{i}=305000\)

Mean salary  \(\begin{align} = \,\frac{{305000}}{{60}}\end{align} \)

Therefore, mean salary of \(60\) workers is \(\rm{Rs.}\, 5083.33. \)
 

  
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