Answer with explanation:
If we arrange the data in ascending order
2, 3, 4,4,5,5,5,6,6,6,7,7,7
Total number of variate in the Data set =13
(A)
If you plot the graph of Data points on two dimensional Coordinate Plane, as how many times they occurs on the line plot , it will be as follows: (2,1), (3,1),(4,2), (5,3),(6,3),(7,3)
First constant from (2,1), to (3,1) , then Increasing from (4,2),to (6,3) , then Constant from (6,3) to (7,3).
If you will look at the variate from mean or median , most of the variate are on the left of Mean or median.So, Data Set is Skewed left.
(B)
Median of the data set is middle most variate in data set.
So,Median
[tex]=\frac{13+1}{2}\\\\=7^{th}[/tex] Observation
Seventh Observation = 5(Median)
(C)
Mean
[tex]=\frac{\text{Sum of all the observations}}{\text{Total number of Observation}}[/tex]
[tex]=\frac{2+3+4+4+5+5+5+6+6+6+7+7+7}{13}\\\\=\frac{67}{13}\\\\=5.15[/tex]
(D) If in the data set , variate 20 is included
Data Set ={2, 3, 4,4,5,5,5,6,6,6,7,7,7,20}
Total number of Variate in the data set =14, which is even.
Median = Mean of Seventh and Eighth term
[tex]=\frac{5+6}{2}\\\\=5.5[/tex]
Difference between Original Median and Median of new data set
=5.5 -5
= 0.5
Mean of new Data set
[tex]=\frac{2+3+4+4+5+5+5+6+6+6+7+7+7+20}{13}\\\\=\frac{87}{14}\\\\=6.214[/tex]
Difference between Original Median and Median of new data set
=6.214 -5.15
= 1.06
Difference in Mean is Larger in Comparison with Median.So, Mean is more affected than Median when variate 20 is added in original Data set.
