1) Given a dataset X=[1,2,3,4,5], calculate the mean, variance and standard deviation.

1. Given a dataset X=[−5,1,65,4,3,5], calculate the median.
2. Without calculating, what is the standard deviation of the dataset X=[1,1,1,1,1]?
3. Given a dataset X=[5,4,6,3,4,25,7,6,3,−1,2], calculate the mean and median. Now remove any data points you think are outliers and recalculate the mean and median.

Please find the answers attached below.

Step-by-step explanation

1 . X = [1 , 2 , 3, 4 , 57 Mean = Xi = ( 1+2+ 3+ 4+5 ) = 3 variance { ( xi - x )' 3 X - 3 = - [4+ 1 + 0 + 1 + 4) 10 = 5 standard deviation = Jvariance = = 1. 4142 X = [ - 5, 1, 65, 4, 3, 57 Arranging, - 5 , 1 , 3 , 4 5 5 , 65 Median is the mid-value, since no. of observations are cron, He is the mean of middle teens. re , 3 + 4 = 1 30 5 3 . X = [ 1 1 , 1, 1 , 1 ] since all the values are the same, there variation ? ie, var lance standard deviation = 0

4 ' X = [ 5 , 4 , 6, 8, 4, 25, 7, 6, 3, -1, 20 Arranging the values, X = [ - 1, 2, 3, 3, 4, 4, 5, 616, 7, 25) mean = xi = 1I X 64 - 5. 8182. Median is the mid- value, 4 is an ourlice since it is much far away from all the other values. Removing 25, x' = [ -1 , 2 , 3 , 3 , 4 , 4 , 5 , 6 , 6 , 7 / mean = 1 x 39 3 .9 10 median = 4+ 4 4 2