def variance(data):
data = check(data)
average = mean(data)
a = []
for i in data:
a.append(sq(subtraction(average, i)))
return mean(a)
def population_correlation_coefficient(list_x, list_y):
total = 0
x = standard_deviation(list_x)
y = standard_deviation(list_y)
for i in range(len(list_x)):
diff_x = subtraction(list_x[i], mean(list_x))
diff_y = subtraction(list_y[i], mean(list_y))
total = total + multiplication(division(diff_x, x), division(
diff_y, y))
return round(
float(
multiplication(division(1, addition(len(list_x), len(list_y))),
total)), 4)
def sampleCorrelation(dataX, dataY):
#dataX= []
#dataY = []
meanX = mean(dataX)
meanY = mean(dataY)
deviationX = standard_deviation(dataX)
deviationY = standard_deviation(dataY)
rNumerator = 0.0
for i in range(len(dataX)):
rNumerator += product(subtraction(dataX[i], meanX),
subtraction(dataY[i], meanY))
rDenominator = product(deviationX, deviationY)
r = division(rNumerator, rDenominator)
return r
def variance(data):
mean_value = mean(data)
terms = [pow((reading - mean_value), 2) for reading in data]
total = 0
for num in terms:
total = addition(total, num)
return total / float(len(data) - 1)
def zscore(data, x):
data = check(data)
m = mean(data)
sd = stddev(data)
num = subtraction(m, x)
result = division(sd, num)
return result
def confidence_interval(numbers):
m = mean(numbers)
confidence_level = 0.95
z = (1-confidence_level) / 2
sd = standard_deviation(numbers)
n = squareroot(len(numbers))
return [subtraction(multiplication(division(n, sd), z), m), addition(multiplication(division(n, sd), z), m)]
def confidenceinterval(a, conf):
n = len(a)
m = mean(a)
sample_stddev = samplestddev(a)
h = marginoferror(a, conf)
return round(m,3), round(m-h,3), round(m+h,3)
def skewness(data):
try:
List1 = []
List2 = []
List3 = []
List4 = []
x = 0
nStddev = stddev(data)
# pprint(nStddev)
nMean = mean(data)
nCount = len(data)
for n in data:
List1.append(subtraction(nMean, n))
# pprint(List1)
for n2 in List1:
List2.append(division(nStddev, n2))
# pprint(List2)
for n3 in List2:
List3.append(n3**3)
# pprint(List3)
for n4 in List3:
x = x + n4
# pprint(x)
# pprint(nCount)
nskewness = division(nCount, x)
# pprint(float(nskewness))
return nskewness
except ZeroDivisionError:
print("Error - Cannot divide by 0")
except ValueError:
print("Error - Invalid data inputs")
def zscore(data):
mean_value = mean(data)
stdev_value = stdev(data)
result = []
for num in data:
result.append((num - mean_value) / stdev_value)
return result
def skew(set):
set = list((1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
me = mean(set)
med = median(set)
std = sd(set)
sk = (3 * (me - med) / std)
return sk
def zScore(data):
x = random.choice(data)
meanData = mean(data)
standardDeviation = standard_deviation(data)
numerator = subtraction(x, meanData)
z = division(numerator, standardDeviation)
return z
def samp_mean(numbers):
ss = random.randint(1, len(numbers))
new_values = getSample(numbers, ss)
n = round(mean(new_values), 2)
actual_mean = round(statistics.mean(new_values),
2) # to compare calculated result
return n, actual_mean
def population_variance(lst):
# below is population variance formula
ttl = 0
for i in range(len(lst)):
ttl += (lst[i] - mean(lst))**2
result = ttl / len(lst)
return round(float(result), 3)
def median(data):
# Validations
empty_list_check(data)
check_for_valid_numbers(data)
data_len = len(data)
data.sort()
# data set has even number of elements
if data_len % 2 == 0:
# find middle
mid = math.trunc(division(2, data_len))
# find middle left value
mid_left = data[mid - 1]
# find middle right value
mid_right = data[mid]
list_of_items = []
list_of_items.insert(0, mid_left)
list_of_items.insert(1, mid_right)
return mean(list_of_items)
else:
# data set has odd number of elements
return data[math.floor(division(2, data_len))]
def standard_deviation(data):
avg = mean(data)
num_values = len(data)
sd1 = 0
for num in data:
sd1 = addition(sd1, squared(subtraction(mean, num)))
return squarerooted(division(num_values, sd1))
def StandardDeviationPopulation(data):
Sum1 = 0
for i in data:
x = abs(i - mean(data))
Sum1 = square(x) + Sum1
n = len(data)
stand_dev = math.sqrt(Sum1) / n
return stand_dev
def confidenceInterval(nums):
length = len(nums)
numsMean = mean(nums)
stanDev = stdDev(nums)
lowerBound = numsMean + 1.96 * (stanDev / math.sqrt(length))
upperBound = numsMean - 1.96 * (stanDev / math.sqrt(length))
returnResult = [lowerBound, upperBound]
return returnResult
def ZScore(num):
z_mean = mean(num)
sdev = sd(num)
z_list = []
for x in num:
z = round(((x - z_mean) / sdev), 6)
z_list.append(z)
return z_list
def variance(data):
n = len(data)
varianceValue = 0
meanData = mean(data)
for i in data:
varianceValue += (i-meanData)**2
varianceValue /= n
return varianceValue
def zscore(numbers):
row_value = 151
sd = psd(numbers)
m = mean(numbers)
result = subtraction(row_value, m)
z_score = division(result, sd)
print(z_score)
return z_score
def StandardDeviationSample(data):
Sum = 0
for i in data:
x = abs(i - mean(data))
Sum = square(x) + Sum
n = len(data)
stand_dev = math.sqrt(Sum / (n - 1))
return stand_dev
def zscore(a):
zmean = mean(a)
sd = stddev(a)
zlist = []
for x in a:
z = round(((x - zmean) / sd), 6)
zlist.append(z)
return zlist
def StdDevPop(data):
Sum2 = 0
for i in data:
x = abs(i - mean(data))
Sum2 = square(x) + Sum2
n = len(data)
stdDev = math.sqrt(Sum2) / n
return stdDev
def StdDevSample(data):
Sum1 = 0
for i in data:
x = abs(i - mean(data))
Sum1 = square(x) + Sum1
n = len(data)
stdDev = math.sqrt(Sum1 / (n - 1))
return stdDev
def _ss(data, c=None):
if c is None:
c = mean(data)
total = total2 = 0
for x in data:
total += (x - c)**2
total2 += (x - c)
total -= total2**2 / len(data)
return total
def conf_interval(data):
x = mean(data)
dev = psd(data)
z = 1.96 # for 95% confidence
standard_error = division(dev, squareroot(len(data)))
conf_upper_level = round(addition(x, multiplication(z, standard_error)), 2)
conf_lower_level = round(subtraction(multiplication(z, standard_error), x), 2)
return conf_upper_level, conf_lower_level
def median(data):
data.sort()
if len(data) % 2 != 0:
center = int((len(data) - 1) / 2)
return data[center]
elif len(data) % 2 == 0:
center1 = int(len(data) / 2)
center2 = int(len(data) / 2) - 1
return int(mean([data[center1], data[center2]]))
def standard_deviation(numbers):
n = len(numbers)
c = 0
t = 0
for i in range(0, n, 1):
c = subtraction(mean(numbers), numbers[i])
t = addition(square(c), t)
x = division((n - 1), t)
return sqrt(x)
def mean_deviation(data):
try:
# 1. find the mean of the data
calculatedMean = mean(data)
distanceArray = []
meanDeviationValue = 0
for item in data:
distanceArray.append(abs(subtraction(item, calculatedMean)))
# 2. find the distance of each value from that mean
# iterate the data list, subtract it from general mean, store it in a list
meanDeviationValue = mean(distanceArray)
return meanDeviationValue
except ZeroDivisionError:
print("Error - Cannot divide by 0")
except ValueError:
print("Error - Invalid data inputs")
def sample_correlation(data, data1):
try:
mean1 = mean(data)
mean2 = mean(data1)
List1 = []
List2 = []
for num in data:
a = subtraction(int(round(mean1, 0)), num)
List1.append(a)
for num in data1:
b = subtraction(mean2, num)
List2.append(b)
c = np.multiply(List1, List2)
cc = 0
for num in c:
cc = cc + num
d = 0
e = 0
# pprint(List1)
# pprint(List2)
for num in List1:
d = d + square(num)
for num in List2:
e = e + square(num)
f = multiplication(int(d), e)
g = square_root(int(f))
h = division(int(g), cc)
# pprint(float(cc))
# pprint(e)
# pprint(f)
# pprint(float(g))
# pprint(str(round(h,9)))
nCorrelation = round(h, 9)
# pprint(nCorrelation)
return nCorrelation
except ZeroDivisionError:
print("Error - Cannot divide by 0")
except ValueError:
print("Error - Invalid data inputs")