Question

Suppose that the data for analysis includes the attribute age. The age values for the data
tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,
33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.
(a) What is the mean of the data? What is the median?
(b) What is the mode of the data? Comment on the data’s modality (i.e., bimodal,
trimodal, etc.).
(c) What is the midrange of the data?
(d) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?
(e) Give the five-number summary of the data.
(f) Show a boxplot of the data.
(g) How is a quantile–quantile plot different from a quantile plot?​

Answer 1

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Southern Illinois University, EdwardsvilleCSCS-490

HW2Han2Yu (1)

Standard DeviationData Mining+1 

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2.Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70. (45 points)(a)What is the mean of the data? What is the median? What is the standard deviation? (15 points)The mean of the data is: x= 809/27 = 29.96 ( or 30)The median is value in the middle of the ordered set since there are an odd number of items in the set. In this case, it’s the 14thitem, or 25The standard deviation σ is the square root of variance, which isWhere N=27 and mean (x) is 30The standard deviation = 12.7Alternatively, we could divide the sum of squares by N-1 = 26 (called bias-corrected deviation).1niixn11niniiiniixnxnxxns1122122])(1[1)(1



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(b) What is the mode of the data? Comment on the data's modality (i.e., bimodal, trimodal, etc.). (5 points)The data is bimodal with 2 highest frequency values: 25 and 35(c)Give the five-number summary of the data. (15 points)Q1 (number at 25%) = 20, Q2 = 35So, the five number are: min, Q1, median, Q3, max, thus: 13, 20, 25, 35, 70.(d) If you plot a boxplot of this data, what will be the box length (in actual number)? What min and max value would the whisker extend to? Is there any outliner (i.e., elements beyond the extreme low and high)? (10 points)Box length = IQR = Q3-Q1 = 35-20 = 151.5 * IQR = 22.5Min boundary: (1stquartile – 1.5*IQR) = -2.5Max boundary: (3rdquartile + 1.5*IQR) = 57.5The whiskers extends to the furthest element with the 1.5&IQR boundary. So, Max whisker extends to largest observed element <= 1.5*IQR+Q3, i.e., 52 (max)