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The following table gives the distribution of the lifetime of 200 wristwatches.

Life Time (In hours) 1000-1500 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500

Number of wristwatches

12 24 56 34 45 56 65

What will be the median lifetime of a wristwatch?

 

Option: 1

3408.82 hours
 


Option: 2

3222.22 hours


Option: 3

3444.22 hours

 


Option: 4

4408.82 hours


Answers (1)

best_answer

option (B)3222.22

The following table gives the distribution of the lifetime of 200 wristwatches.

Life Time (In hours) 1000-1500 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500

Number of wristwatches

12 24 56 34 45 56 65

From the given table, we have the frequency distribution table as,

Life Time (In hours) 1000-1500 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500

Number of wristwatches

12 24 56 34 45 56 65
Cumulative frequency 12 36 92 126 171 227 292

 

We have, 

 

\mathrm{n=\frac{N}{2}}

\mathrm{\Rightarrow n=\frac{292}{2}}

\mathrm{\Rightarrow n=146}

Here, the cumulative frequency just greater than 146 is 171 and the corresponding class is 3000-3500.

Therefore, the median class is 3000-3500.

We know the general formula for median of grouped data is,

\mathrm{\text{Median}=\ l+(h\times \frac{\frac{N}{2}-cf}{f}) }

Where, 

\mathrm{l}=lower limit of the median class, 

\mathrm{h}=size of the median class, 

\mathrm{f}= frequency of the median class, 

\mathrm{N}= sum of frequencies and 

\mathrm{cf}=cumulative frequency of the class just preceding the median class.

We have,

\mathrm{\ l=3000,\ h=500,\ f=45, \ N=292, \ cf=126 }

Calculating the median, we get,

\mathrm{\text{Median}=\ 3000+(500\times \frac{\frac{292}{2}-126}{45}) }

\mathrm{\text{Median}=\ 3000+(500\times \frac{20}{45}) }

\mathrm{\text{Median}=\ 30+\ 222.22 }

\mathrm{\Rightarrow \text{Median}=3222.22 }

Therefore, the median lifetime of a wristwatch = 3222.22 hours.

 

 

Posted by

Ajit Kumar Dubey

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