For every quantitative attribute, compute exactly what percentage of instances are within 1, 2 and 3 standard deviations of the mean. Don not use Chebychev’s Theorem of the Empirical Rule.

Question

This answer has to be in python codes that is used in the jupyter notebook to execute and find the answer.

example if the question is : Column : ‘Attribute’

and Attribute = ( 1,2,2,2,2,1,1,1,2,2,1,1,1,2,2,1,4,1,1,1,2,1,1,1,1,1,1,3 )

the numbers are it’s rows in the column and solve the above question with this given data....

Answer 1

import math

#returns: mean,min,max,variance,stdDev

def CalcStats( stats):

results = []

N = len(stats)

print('N=' + str(N))

sum=0

max=-math.inf

min=math.inf

for i in range(int(N)):

sum = sum + float(stats[i])

if float(stats[i])<min:

min = float(stats[i])

if float(stats[i])>max:

max = float(stats[i])

print('sum=' + str(sum))

mean = float(sum)/int(N)

results.append(mean)

results.append(min)

results.append(max)

return results

def Variance(A,meanAvg,n):

Variances = []

sumDevSqr=0

sumXSqr=0

sumDev=0

print(' X devX dev^2 X^2 ')

for i in range(int(n)):

X = float(A[i])

deviation = float(X)-float(meanAvg)

deviationSquared = float(deviation)*float(deviation)

xSqr = float(X) * float(X)

sumDevSqr = float(sumDevSqr) + float(deviationSquared)

sumXSqr = float(sumXSqr) + float(xSqr)

sumDev = float(sumDev) + float(deviation)

print(' ' + str(X) + ' ' + str(deviation) + ' '

+ str(deviationSquared) + ' ' + str(xSqr))

print('-----------------------------------------')

xSum = float(meanAvg)*int(n)

print(str(xSum) + ' ' + str(sumDev) + ' ' + str(sumDevSqr) + ' ' + str(sumXSqr))

varByDef = float(sumDevSqr)/(int(n)-1)

varByShortcut = (float(sumXSqr) - int(n)*float(meanAvg)*float(meanAvg))/(n-1)

Variances.append(varByDef)

Variances.append(varByShortcut)

return Variances

#-----------------------------------

A=[2,5,8,11,13,15,17,20]

results = CalcStats(A)

print(results)

meanAvg = results[0]

print('mean average = ' + str(meanAvg))

print(' min = ' + str(results[1]))

print(' max = ' + str(results[2]))

variances = Variance(A,meanAvg,8)

print('variance = ')

print(variances)

stndDev = math.sqrt(float(variances[0]))

print('standard deviation is ' + str(stndDev))