Answer with explanation:
Let me start answering this Question like this.
Why Median came into existence because Mean was not good enough to provide better solution to Statistical Data Set.
What, is Median.Median of a discrete data set ,is Middle value in the data set when arranged in ascending or descending order.Suppose you have to find whether wages of Employee in certain Organization is appropriate or not.You will use two measure of variation for that Purpose: 1. Mean 2.Median
Consider Bar graph of Data set 1
Variate in set builder form ={10,15,20,25,30,35,30,25,20,15,10}
When arranged in ascending order ={10,10,15,15,20,20,25,25,30,30,35}=11(Odd)
Mean
[tex]=\frac{235}{11}\\\\=21\frac{4}{11}[/tex]
Median =Mid value =20
Median - Smallest variate =20 -10=10
Largest Variate - Median =35-20=15
→→→Consider Bar Graph of Data set 2
Variate in set builder form ={22,18,20,26,30,28,20,9,9,5,4,3,3,2}
When arranged in ascending order ={2,3,3,4,5,9,9,18,20,20,22,26,28,30}=14(Even)
Mean
[tex]=\frac{199}{14}\\\\=14\frac{3}{14}[/tex]
Median
[tex]=\frac{9+18}{2}\\\\13.5[/tex]
Median - Smallest variate =13.5 - 2=11.5
Largest Variate - Median =30 -13.5=16.5
→→Consider Bar Graph of Data set 3
Variate in set builder form ={4,3,4,,4,5,5,5,4,5,5}
When arranged in ascending order ={3,4,4,4,4,5,5,5,5,5}=10(Even)
Mean
[tex]=\frac{44}{10}\\\\=4.4[/tex]
Median
[tex]=\frac{4+5}{2}\\\\4.5[/tex]
Median - Smallest variate =4.5 -3=1.5
Largest Variate - Median =5-4.5=0.5
Consider Bar graph of Data set 4
Variate in set builder form ={11,12,13,14,15,18,19,24,28,15,12,11}
When arranged in ascending order ={11,11,12,12,13,14,15,15,18,19,24,28}=12(even)
Mean
[tex]=\frac{192}{12}\\\\=16[/tex]
Median
[tex]=\frac{14+15}{2}\\\\14.5[/tex]
Median - Smallest variate =14.5 - 11=3.5
Largest Variate - Median =28 - 14.5=13.5
Drawing Box plot of four data set
Found that, for data set 3, median lies in the center.
Option 2 and Option 3
