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Contents

Conditionals and Loops

from datascience import *
import numpy as np

%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
import warnings
warnings.simplefilter(action='ignore', category=np.VisibleDeprecationWarning)

Booleans and Comparison Operators

3 > 1

True

type(3 > 1)

bool

3 = 3

  File "/var/folders/md/kwd9nc_d2ns0hw9wsvdrnt2c0000gn/T/ipykernel_4262/3802935557.py", line 1
    3 = 3
    ^
SyntaxError: cannot assign to literal

3 == 3

True

x = 5
y = 12

x == 7

False

y - x

7

4 < y - x <= 6

False

4 < y - x

True

y - x <= 6

False

True and False

False

True or False

True

True and True

True

Monopoly

monopoly = Table().read_table("data/monopoly.csv")
monopoly

Name	Space	Color	Position	Price	PriceBuild	Rent	RentBuild1	RentBuild2	RentBuild3	RentBuild4	RentBuild5	Number
Go	Go	None	0	0	0	0	0	0	0	0	0	0
Mediterranean Avenue	Street	Brown	1	60	50	2	10	30	90	160	250	2
Community Chest	Chest	None	2	0	0	0	0	0	0	0	0	0
Baltic Avenue	Street	Brown	3	60	50	4	20	60	180	320	450	2
Income Tax	Tax	None	4	200	0	200	0	0	0	0	0	0
Reading Railroad	Railroad	None	5	200	0	25	0	0	0	0	0	0
Oriental Avenue	Street	LightBlue	6	100	50	6	30	90	270	400	550	3
Chance	Chance	None	7	0	0	0	0	0	0	0	0	0
Vermont Avenue	Street	LightBlue	8	100	50	6	30	90	270	400	550	3
Connecticut Avenue	Street	LightBlue	9	120	50	8	40	100	300	450	600	3

... (30 rows omitted)

tiny_monopoly = monopoly.where('Color', are.not_equal_to('None'))
tiny_monopoly = tiny_monopoly.where('Space', are.containing('Street'))
tiny_monopoly = tiny_monopoly.select('Name', 'Color', 'Price')
tiny_monopoly = tiny_monopoly.sort('Name')  

tiny_monopoly.show()

Name	Color	Price
Atlantic Avenue	Yellow	260
Baltic Avenue	Brown	60
Boardwalk	Blue	400
Connecticut Avenue	LightBlue	120
Illinois Avenue	Red	240
Indiana Avenue	Red	220
Kentucky Avenue	Red	220
Marvin Gardens	Yellow	280
Mediterranean Avenue	Brown	60
New York Avenue	Orange	200
North Carolina Avenue	Green	300
Oriental Avenue	LightBlue	100
Pacific Avenue	Green	300
Park Place	Blue	350
Pennsylvania Avenue	Green	320
St. Charles Place	Pink	140
St. James Place	Orange	180
States Avenue	Pink	140
Tennessee Avenue	Orange	180
Ventnor Avenue	Yellow	260
Vermont Avenue	LightBlue	100
Virginia Avenue	Pink	160

Suppose we only have 220 dollars. How many properties could we buy for exactly 220 dollars?

price = tiny_monopoly.column("Price")
price

array([260,  60, 400, 120, 240, 220, 220, 280,  60, 200, 300, 100, 300,
       350, 320, 140, 180, 140, 180, 260, 100, 160])

price == 220

array([False, False, False, False, False,  True,  True, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False])

sum(price==220)

2

np.count_nonzero(price == 220)

2

How many properties could we buy for less than or equal to 200 dollars?

price

array([260,  60, 400, 120, 240, 220, 220, 280,  60, 200, 300, 100, 300,
       350, 320, 140, 180, 140, 180, 260, 100, 160])

price <= 200

array([False,  True, False,  True, False, False, False, False,  True,
        True, False,  True, False, False, False,  True,  True,  True,
        True, False,  True,  True])

np.count_nonzero(price <= 200)

11

How many of the Monopoly spaces are light blue?

sum(monopoly.column("Color") == "LightBlue")

3

Conditional Statements

def price_rating(price):
    if price < 100:
        print("Inexpensive")
        
price_rating(50)

Inexpensive

price_rating(500)

def price_rating(price):
    if price < 100:
        print("Inexpensive")
    else:
        print("Expensive")

price_rating(500)

Expensive

# return a value instead of printing
def price_rating(price):
    if price < 200:
        return "Inexpensive"
    elif price < 300:
        return "Expensive"
    elif price < 400:
        return "Very Expensive"
    else:
        return "Outrageous"

ratings = tiny_monopoly.apply(price_rating, 'Price')
ratings

array(['Expensive', 'Inexpensive', 'Outrageous', 'Inexpensive',
       'Expensive', 'Expensive', 'Expensive', 'Expensive', 'Inexpensive',
       'Expensive', 'Very Expensive', 'Inexpensive', 'Very Expensive',
       'Very Expensive', 'Very Expensive', 'Inexpensive', 'Inexpensive',
       'Inexpensive', 'Inexpensive', 'Expensive', 'Inexpensive',
       'Inexpensive'], dtype='<U14')

rated_monopoly = tiny_monopoly.with_columns("Cost Rating", ratings)
rated_monopoly

Name	Color	Price	Cost Rating
Atlantic Avenue	Yellow	260	Expensive
Baltic Avenue	Brown	60	Inexpensive
Boardwalk	Blue	400	Outrageous
Connecticut Avenue	LightBlue	120	Inexpensive
Illinois Avenue	Red	240	Expensive
Indiana Avenue	Red	220	Expensive
Kentucky Avenue	Red	220	Expensive
Marvin Gardens	Yellow	280	Expensive
Mediterranean Avenue	Brown	60	Inexpensive
New York Avenue	Orange	200	Expensive

... (12 rows omitted)

rated_monopoly.where('Cost Rating', 'Inexpensive')

Name	Color	Price	Cost Rating
Baltic Avenue	Brown	60	Inexpensive
Connecticut Avenue	LightBlue	120	Inexpensive
Mediterranean Avenue	Brown	60	Inexpensive
Oriental Avenue	LightBlue	100	Inexpensive
St. Charles Place	Pink	140	Inexpensive
St. James Place	Orange	180	Inexpensive
States Avenue	Pink	140	Inexpensive
Tennessee Avenue	Orange	180	Inexpensive
Vermont Avenue	LightBlue	100	Inexpensive
Virginia Avenue	Pink	160	Inexpensive

rated_monopoly.where('Cost Rating', 'Outrageous')

Name	Color	Price	Cost Rating
Boardwalk	Blue	400	Outrageous

Simulation and Loops

Think-pair-share

Suppose your friend proposes that you switch your electronic version of Monopoly so players roll one dice and multiply its value by two instead rather than the more standard way of rolling two dice and summing their values.

Which scenario will give you a higher score on average?

• Option A. Roll 2 dice and sum their values.

• Option B. Roll one dice and multiply it’s value by two.

Random Selection

dice = np.arange(1,7)
dice

array([1, 2, 3, 4, 5, 6])

Here, np.random.choice randomly picks one item from the array and it is equally likely to pick any of the items.

np.random.choice(dice)

5

We can repeat the process by calling a second argument.

np.random.choice(dice, 10)

array([1, 4, 4, 4, 2, 6, 2, 3, 5, 2])

rolls = np.random.choice(dice,100)
sum(rolls == 6)

19

np.mean(rolls)

3.51

Simulating the Question

N = 1000000
option_a = np.random.choice(dice, N) + np.random.choice(dice, N)
option_b = 2 * np.random.choice(dice, N)

print("Option A Mean: ", np.mean(option_a))
print("Option B Mean: ", np.mean(option_b))

Option A Mean:  7.001924
Option B Mean:  7.001088

samples = Table().with_columns("Option A", option_a, "Option B", option_b)
samples.hist("Option A", bins=np.arange(0,14))
samples.hist("Option B", bins=np.arange(0,14))

samples.hist(bins=np.arange(0,14))

Think-Pair-Share 2

If you flip a coin 100 times, what are the odds you get between 40 and 60 heads?

Simulating One Trial

coin = make_array('heads', 'tails')

np.random.choice(coin)

'tails'

tosses = np.random.choice(coin, 100)
tosses

array(['tails', 'heads', 'tails', 'tails', 'tails', 'tails', 'heads',
       'tails', 'heads', 'tails', 'heads', 'tails', 'tails', 'tails',
       'heads', 'tails', 'heads', 'tails', 'tails', 'tails', 'tails',
       'tails', 'heads', 'tails', 'heads', 'tails', 'heads', 'tails',
       'heads', 'heads', 'tails', 'heads', 'tails', 'heads', 'tails',
       'heads', 'heads', 'tails', 'heads', 'heads', 'tails', 'heads',
       'tails', 'tails', 'heads', 'tails', 'heads', 'tails', 'heads',
       'heads', 'heads', 'heads', 'tails', 'heads', 'heads', 'tails',
       'tails', 'heads', 'tails', 'tails', 'heads', 'tails', 'heads',
       'tails', 'heads', 'tails', 'tails', 'tails', 'tails', 'tails',
       'heads', 'tails', 'heads', 'heads', 'tails', 'heads', 'heads',
       'tails', 'tails', 'heads', 'tails', 'heads', 'heads', 'heads',
       'heads', 'tails', 'heads', 'heads', 'tails', 'heads', 'heads',
       'heads', 'heads', 'heads', 'tails', 'tails', 'heads', 'heads',
       'heads', 'heads'], dtype='<U5')

sum(tosses == 'heads')

51

All in one cell: run it a bunch!

sum(np.random.choice(coin, 100) == 'heads')

55

Running Many Trials: For Loops

for name in ['Katie', 'Steve']:
    print(name)

Katie
Steve

for i in np.arange(0,10):
    print("iteration", i)

iteration 0
iteration 1
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9

# Steve: Important for prelab to show one loop that accumulates a value...
total = 0
for i in np.arange(0,10):
    total = total + i
total

45

for i in np.arange(0,10):
    print(sum(np.random.choice(coin, 100) == 'heads'))

51
56
47
47
46
41
50
52
41
54

Appending to an array of outcomes

outcomes = make_array()

One simulation: run it a bunch!

num_heads = sum(np.random.choice(coin, 100) == 'heads')
outcomes = np.append(outcomes, num_heads)
outcomes

array([54.])

All in one cell:

outcomes = make_array()
number_simulations = 10000
for i in np.arange(0,number_simulations):
    num_heads = sum(np.random.choice(coin, 100) == 'heads')
    outcomes = np.append(outcomes, num_heads)
    
outcomes

array([45., 49., 50., ..., 58., 45., 51.])

simulated_results = Table().with_column('Heads in 100 flips', outcomes)

simulated_results.hist(bins=np.arange(30, 70, 1))

target_range = simulated_results.group("Heads in 100 flips").where("Heads in 100 flips", are.between(40,60))
target_range

Heads in 100 flips	count
40	124
41	176
42	213
43	287
44	355
45	474
46	554
47	658
48	737
49	815

... (10 rows omitted)

sum(target_range.column("count")) / simulated_results.num_rows

0.9558