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  • What will be the median of the following data? Class 0-10 <td

What will be the median of the following data?

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 3 4 5 6 3 2 1

 

Option: 1

50


Option: 2

60


Option: 3

30


Option: 4

80


Answers (1)

best_answer

Option (c) 30

The given data table is,

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 3 4 5 6 3 2 1

 

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

class Frequency \mathrm{f_{i}} Mid value\mathrm{x_{i} } cumulative frequency \mathrm{f_{i}x_{i} }
0-10 3

5

 3 15
10-20 4 15 7 60
20-30 5 25 12 125
30-40 6 35 18 210
40-50 3 45 21 135
50-60 2 55 23 110
60-70 1 65 24 65
  \mathrm{\sum_{}^{}f_{i}=24 }     \mathrm{\sum_{}^{}f_{i}x_{i}=720}

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

\mathrm{\Rightarrow n=\frac{24}{2}}

\mathrm{\Rightarrow n=12}

Here, the cumulative frequency just greater than 12 is 18 and the corresponding class is 30-40

Therefore, the median class is 30-40.

\mathrm{\therefore \ l=30,\ h=10,\ f=6, \ N=24, \ cf=12 }

Calculating the median, we get,

\mathrm{\text{Median}=\ 30+(10\times \frac{\frac{24}{2}-12}{6}) }

\mathrm{\text{Median}=\ 30+(10\times \frac{12-\ 12}{6})}
\mathrm{\text{Median}=\ 30+(10\times \frac{0}{6}) }
\mathrm{\Rightarrow \text{Median}=30 }

 

 

Posted by

Anam Khan

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