Unit 5 - Exploring bivariate numerical data (2026 Jun 21)

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xmean = 24.1
ymean = 12.9
sx = 12
sy = 16.2
r = 0.9

m = r * (sy/sx)
c = ymean - m*xmean

print("m, c:", round(m, 3), round(c, 3))

# KA's Answers: 1.22, -16.38


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Quiz on "Modeling data distributions" (Unit 4, Jun 14th 2026)

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1:

Code:

mean = 170.4
sd = 10

l = 145
lz = (l - mean) / sd
print(lz)

import statistics
lz_area = statistics.NormalDist(mu=0, sigma=1).cdf(lz)
print(lz_area)

h = 171
hz = (h - mean) / sd
print(hz)

hz_area = statistics.NormalDist().cdf(hz)

area_req = round(hz_area - lz_area,4)
print(area_req)

---

2:

mean = 80
sd = 9

proportion = 0.4

import statistics
z = statistics.NormalDist().inv_cdf(proportion)

print(z)

x = z * sd + mean

print(x)

---

3:

Code:

mean = 13.1
sd = 1.5

sd1 = (mean - sd, mean + sd)
print(sd1)

sd2 = (mean - 2 * sd, mean + 2 * sd)
print(sd2)

sd3 = (mean - 3 * sd, mean + 3 * sd)
print(sd3)

sd2_area = 0.95
sd3_area = 0.997

area_req = (sd3_area - sd2_area) / 2

print(area_req)

percentage_wise = round(area_req * 100, 4)
print(percentage_wise)

out = """
(11.6, 14.6)
(10.1, 16.1)
(8.6, 17.6)
0.02350000000000002
2.35
"""

---

4:

Code:

b = 2
h = 0.6

area = 0.5 * b * h

percentage_of_area = area * 100

print(percentage_of_area)

---

5:

Code:

mean_sales = 8000
sd_sales = 1500

mean_salary = 2000 + 0.3 * mean_sales

sd_salary = sd_sales * 0.3

print("mean_salary, sd_salary")
print(mean_salary, sd_salary)

---

6:

---

7:

area = 1
b = 6
h = area * 2 / b
print(h)

---

8:

def area_of_trapezium(b1, b2, h):
    return 0.5 * (b1 + b2) * h

b1 = 0.5
b2 = 0.75
h = 1

a = area_of_trapezium(b1, b2, h)
print(a)

print(round(a*100, 4))


b1 = 0.25
b2 = 0.5
h = 1

a = area_of_trapezium(b1, b2, h)
print(a)

print(round(a*100, 4))

---

9:

---

10:

mean = 1497
sd = 322

proportion = 0.85

import statistics
z = statistics.NormalDist().inv_cdf(proportion)

x = z * sd + mean

print(round(x, 4))

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Tags: Python,Mathematical Foundations for Data Science,Data Analytics,

What is a Class Factory?

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explain this text from a book in layman terms (it's completely bouncing off of me):

The default class factory is type. When you write

class Dog:
    pass

Python roughly does:

Dog = type('Dog', (), {})

---

This is one of those Python lines that looks mysterious until you realize it's just showing what Python does behind the scenes.

Let's start with the code you normally write:

Python
class Dog:
    pass

Most people think this creates a class using some special Python magic.

What actually happens is that Python asks another object called type to create the class.

Behind the scenes, Python roughly does:

Python
Dog = type('Dog', (), {})

Let's decode each piece.

---

Step 1: What is type?

You've probably used it like this:

Python
x = 5
print(type(x))

Output:

Python
<class 'int'>

So it seems like type() tells you the type of an object.

But here's the twist:

Python
print(type(int))

Output:

Python
<class 'type'>

Even classes themselves are objects.

And the thing that creates classes is type.

Think of it like this:

Dog object  <-- created by -- type
Cat object  <-- created by -- type
Person object <-- created by -- type

type is the "class factory."

---

Step 2: The first argument

Python
type('Dog', (), {})

First argument:

Python
'Dog'

This is simply the class name.

Equivalent to:

Python
class Dog:
    pass

---

Step 3: The second argument

Python
()

This is a tuple containing parent classes.

Example:

Python
class Dog:
    pass

has no explicit parent class, so:

Python
()

means "no parent classes specified."

Another example:

Python
class Dog(Animal):
    pass

would roughly become:

Python
Dog = type('Dog', (Animal,), {})

Notice the tuple contains Animal.

---

Step 4: The third argument

Python
{}

This dictionary contains everything inside the class body.

Example:

Python
class Dog:
    species = "Canine"

    def bark(self):
        print("Woof")

becomes approximately:

Python
Dog = type(
    'Dog',
    (),
    {
        'species': 'Canine',
        'bark': bark
    }
)

The dictionary is basically:

attribute name -> value
method name    -> function

---

Visualizing the process

When Python sees:

Python
class Dog:
    pass

it internally thinks something like:

1. Create an empty dictionary {}
2. Put class variables and methods into it
3. Call type()
4. Store the result in Dog

So:

Python
class Dog:
    pass

is roughly:

Python
Dog = type('Dog', (), {})

---

Proof

These two are essentially equivalent:

Normal syntax

Python
class Dog:
    def bark(self):
        print("Woof")

Using type

Python
def bark(self):
    print("Woof")

Dog = type(
    'Dog',
    (),
    {'bark': bark}
)

Both work:

Python
d = Dog()
d.bark()

Output:

Python
Woof

---

The big idea

There are objects, classes, and something that creates classes.

Think of a car factory:

Factory ---> creates Cars

In Python:

type ---> creates Classes
Class ---> creates Objects

Example:

Python
Dog = type('Dog', (), {})

type
  ↓
Dog class
  ↓
Dog()
  ↓
dog object

This idea becomes important later when learning metaclasses, because a metaclass is simply a custom replacement for type that can control how classes themselves are created.

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