Chapter 2: Organization and Description of Data¶
Example, page-13¶
In [1]:
#Variable declaration
time=[0.107,0.196,0.021,0.283,0.179,0.854,0.58,0.19,7.3,1.18,2.0] # Time in Seconds
neutrinos=[1,1,1,1,1.1,1,1,1.2,1,1,1]
#Calculation
from scipy import *
from pylab import *
%matplotlib inline
#Results
scatter(time,neutrinos)
title("Dot Diagram")
xlabel("$time(s)$")
ylabel("$neutrinos$")
Out[1]:
Example, page-14¶
In [2]:
#Variable declaration
sample1 = [0.27,0.35,0.37] # Copper content-1
sample2 = [0.23,0.15,0.25,0.24,0.30,0.33,0.26] # Copper content-2
Yvalue1 = [1,1,1]
Yvalue2 = [1,1,1,1,1,1,1]
#Calculation
from scipy import *
from pylab import *
%matplotlib inline
#Results
scatter(sample1,Yvalue1,c='b',marker='o')
scatter(sample2,Yvalue2,c='r',marker='o')
title("Dot Diagram")
xlabel("$Copper Content$")
Out[2]:
Example, Page-16¶
In [3]:
#Variable declaration
l = [205,245,285,325,365,405] # intervels
Marks = []
#Calculation
from scipy import *
from pylab import *
for i in range(0,5):
Marks.append((l[i]+l[i+1])/2)
#Results
print "Class Average: "
for each in Marks:
print each," "
print "Class Interval: ",l[1]-l[0]
Example, Page-16¶
In [4]:
#Variable declaration
l = [205,245,285,325,365,405] # intervels
frequency = [3,11,23,9,4]
cal = []
sum1 = 0
#Calculation
from scipy import *
from pylab import *
for i in range(1,6):
for j in range(0,i):
sum1 = sum1 + frequency[j]
cal.append(sum1)
sum1 = 0
#Results
print "Cumulative Frequency: "
for i in range(0,5):
print "(",l[i],",",l[i+1],"]"," ",cal[i]
Example, Page-19¶
In [5]:
#Variable declaration
l = [2808, 4201, 3848, 9112, 2082, 5913, 1620, 6719, 21657,
3072, 2949, 11768, 4731, 14211, 1583, 9853, 78811, 6655,
1803, 7012, 1892, 4227, 6583, 15147, 4740, 8528, 10563,
43003, 16723, 2613, 26463, 34867, 4191, 4030, 2472, 28840,
24487, 14001, 15241, 1643, 5732, 5419, 28608, 2487, 995,
3116, 29508, 11440, 28336, 3440]
height = [0,0,0,0,0,0,0,0,0,0,0]
X = [0,10000,20000,30000,40000,50000,60000,70000,80000,90000,100000]
#Calculation
from scipy import *
from pylab import *
%matplotlib inline
for each in l:
height[each/10000 ] = height[each/10000 ] + 1
#Results
bar(X,height,width=10000,fill=False)
xlabel("$Time(microseconds)$")
ylabel("$ClassFrequency$")
Out[5]:
Example, page-25¶
In [9]:
#Variable declaration
l=[15,14,2,27,13] #list of numbers of meals claimed
#Calculation
from scipy import *
Median=median(l) #median of all entries
Mean=round(mean(l),2) #mean of all entries
#Results
print "mean: ",Mean,"meals"
print "median: ",int(Median),"meals"
Example, page-25¶
In [18]:
#Variable declaration
l=[11,9,17,19,4,15] #list of numbers of e-mail received for six day
#Calculation
from scipy import *
Median=median(l) #median of all entries
Mean=round(mean(l),2) #mean of all entries
#Results
print "mean: ",Mean,"requests"
print "median: ",int(Median),"requests"
Example, page-27¶
In [19]:
#Variable declaration
l=[0.6,1.2,0.9,1.0,0.6,0.8] #list of delay times
k=0
#Calculation
from scipy import *
from pylab import *
Mean=round(mean(l),4)
for each in l:
k+=(each-Mean)**2
ssquare=round(k/(len(l)-1),3) # Sample Variance (in minute square)
#Results
print "Sample Variance: ",ssquare,"(minute square)"
Example, page-28¶
In [20]:
#Variable declaration
l=[0.6,1.2,0.9,1.0,0.6,0.8] #list of delay times
k=0
#Calculation
from scipy import *
from pylab import *
Mean=round(mean(l),4)
for each in l:
k+=(each-Mean)**2
s=sqrt(round(k/(len(l)-1),3)) # Standard deviation (in minute)
s=round(s,2)
#Results
print "Standard deviation: ",s,"minute"
Example, page-29¶
In [21]:
#Variable declaration
stddev1 = 0.0152 #standard deviation for ball bearing (in mm)
mean1 = 3.92 #mean for ball bearing (in mm)
stddev2 = 0.0086 #standard deviation for spring (in inch)
mean2 = 1.54 #mean for spring (in inch)
#Calculation
from scipy import *
from pylab import *
cof_var1 = round((stddev1/mean1)*100,3) # coff of variation for ball bearing in %
cof_var2 = round((stddev2/mean2)*100,3) # coff of variation for spring in %
#Results
if cof_var1<cof_var2:
print "First instrument is more precise"
elif cof_var1>cof_var2:
print "Second instrument is more precise"
else:
print "both instruments are equal precise"
Example, page-30¶
In [22]:
#Variable declaration
l = [221, 234, 245, 253, 265, 266, 271, 272, 274, 276,
276, 276, 278, 284, 289, 290, 290, 292, 292, 296,
297, 298, 300, 303, 304, 305, 305, 308, 308, 309,
310, 311, 312, 314, 315, 315, 323, 330, 333, 336,
337, 338, 343, 346, 355, 364, 366, 373, 390, 391]
#Calculation
from scipy import *
from pylab import *
np = len(l)*0.25 # np-losition in list l[],for first quartile p=1/4
Q1 = l[12] # as np=12.5,so we round up to 13th
np = len(l)*0.5 #for second quartile p=1/2
np=int(np)
Q2 = (l[np-1] + l[np])*0.5 # Average of 25th and 26th
np = len(l)*0.75 #for third quartile p=3/4
Q3=l[37] # round up to 38th
np = len(l)*0.93 #for 93rd percentile p=0.93
Q93=l[46] # round up to 47th
#Results
print "First quartile Q1: ",Q1,"nm"
print "Second quartile Q2: ",Q2,"nm"
print "Third quartile Q3: ",Q3,"nm"
print "93rd quartile Q93: ",Q93,"nm"
Example, page-31¶
In [23]:
#Variable declaration
l = [221, 234, 245, 253, 265, 266, 271, 272, 274, 276,
276, 276, 278, 284, 289, 290, 290, 292, 292, 296,
297, 298, 300, 303, 304, 305, 305, 308, 308, 309,
310, 311, 312, 314, 315, 315, 323, 330, 333, 336,
337, 338, 343, 346, 355, 364, 366, 373, 390, 391] #list of all height entries
#Calculation
from scipy import *
from pylab import *
np = len(l)*0.25 # np-losition in list l[],for first quartile p=1/4
Q1 = l[12] # as np=12.5,so we round up to 13th
np = len(l)*0.5 #for second quartile p=1/2
np = int(np)
Q2 = (l[np-1] + l[np])*0.5 # Average of 25th and 26th
np = len(l)*0.75 #for third quartile p=3/4
Q3 = l[37] # round up to 38th
rng = max(l)-min(l) #range of height
int_rng = Q3-Q1 #interquartile range of height
#Results
print "range : ",rng,"nm"
print "interquartile range : ",int_rng,"nm"
Example, Page-32¶
In [24]:
#Variable declaration
x = [0.021, 0.107, 0.179, 0.190, 0.283, 0.580, 0.854, 1.18, 2.00, 7.30]
#Calculation
from scipy import *
from pylab import *
import matplotlib.pyplot as plt
%matplotlib inline
plt.boxplot(x,vert=False)
xlabel("$Time(s)$")
Out[24]:
Example, Page-34¶
In [25]:
#Variable declaration
l = [19.7, 21.5, 22.5, 22.2, 22.6,
21.9, 20.5, 19.3, 19.9, 21.7,
22.8, 23.2, 21.4, 20.8, 19.4,
22.0, 23.0, 21.1, 20.9, 21.3]
sum1 = 0.0
#Calculation
from scipy import *
from pylab import *
Mean=sum(l)/len(l)
for each in l:
sum1 = sum1 + each*each
variance = (sum1 - (pow(sum(l),2.0)/len(l)))/(len(l)-1) # variance
variance= round(variance,3)
#Results
print "mean: ",Mean,"mpg"
print "variance: ",variance
Example, page-35¶
In [26]:
#Variable declaration
x = array([[225,3],[265,11],[305,23],[345,9],[385,4]])
temp1 = 0
temp2 = 0
#Calculation
from scipy import *
from pylab import *
from numpy import *
for i in range(0,5):
temp1 = temp1 + x[i][0]*x[i][1]
Mean = temp1/sum(x[0:5,1]) # mean=sum(x(i)*f(i))/sum(f(i) class average
for i in range(0,5):
temp2 = temp2 + x[i][0]*x[i][0]*x[i][1]
variance = (temp2 - (temp1**2) / sum(x[0:5,1])) / float(sum(x[0:5,1])-1) # variance
variance=round(variance,2)
std_dev=round(sqrt(variance),1) # standard deviation
#Results
print "mean: ",Mean
print "variance: ",variance
print "standard deviation: ",std_dev