1. Use the following stock price data (in dollar) for the questions: 14, 20, 13,

Question

1. Use the following stock price data (in dollar) for the questions: 14, 20, 13, 18. 5.9. 15,7, 14,75, 12, 10. 16, 8 a. Find the min-max normalized stock price for the stock worth $20 Compute the Z-score standardized stock price for the stock worth $20 Find the decimal scaling stock price for the stock worth $20 b. c. d. Calculate the skewness of the stock price data. e. Is the distribution symmetric? If not, propose some methods to make it more symmetric, and verify your proposed methods. f. Check if there is any outlier, using the Z-score method. Check if there is any outlier, using the IQR method. g. h. Investigate how the outlier affects the mean and median by doing the following: i. Compare the mean score and the median score, with and without the outlier a. x'-(x-Xin / (Xn(20 5)/ (75-5)-0.214 b. Sample mean usingR- 16.86; sample standard deviation using R- 17.27 Z-score for $20 x'20-(x-3)/s (20 16.86)/ (17.27) 0.1818 c. Decimal scaling: x*-x/10-20 1020 = 0.2 d. Median using R= 13.5 ; Skewness-(3 * (mean-median)(st-dev)) (3*(16.86-13.5))/(17.27)-0.584

Explanation / Answer

Sol:

IQR method is

Any value below

Q1-1.5IQR

and any value above

Q3+1.5 IQR is an outlier

Use Follow R code to get five number summary

stockprice <- c(14,20,13,18,5,9,
15,7,14,75,12,10,16,8)
fivenum(stockprice)

min=5

Q1=9

Q2=13.5

Q3=16

Max=75

IQR=Q3-Q1=16-9=7

Q1-1.5IQR=9-1.5*7=-1.5

Q3+1.5IQR=16+1.5*7=26.5

any value below -1.5 and any value above 26.5 is an outlier

All values are between limits except 75

which is above 26.5

75 is an outlier

Solutiong:

outliers affects mean

median is not influenced by outlier

Solutioni:

stockprice <- c(14,20,13,18,5,9,
15,7,14,75,12,10,16,8)
  
mean(stockprice)
median(stockprice)

mean= 16.85714

median=13.5

Now remove outlier 75

stockprice_withoutoutlier <- c(14,20,13,18,5,9,
15,7,14,12,10,16,8)
  
mean(stockprice_withoutoutlier)
median(stockprice_withoutoutlier)

mean without outlier=12.38462

median without outlier=13

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