3: Data Types

Evaluating Expressions with Numbers

• When an expression with both int data type and float data type is evaluated, the result is a float.

num1 = 6.2
num2 = 5
difference = num1 - num2
print("Type of num1:", type(num1))
print("Type of num2:", type(num2))
print("Type of the difference:", type(difference))

Output?

• When evaluating expressions with float data types, the result may be off by the last one or two digits. This is because some decimal numbers can have infinitely many digits, but data on a computer can only be stored with a finite number of bits (typically 64 bits), so some decimal numbers will have a tiny rounding error.

For most calculations in data science, the tiny rounding error is not a problem since the input data is limited to a certain number of significant digits, therefore we always round the output to the same number of significant digits, which means the last one or two digits in the output can be ignored.

import math

# Suppose we have an original input number which is precise to
# 1 digit after the decimal point:
num = 2.0

# Using Python's square root function, we find the square root of num.
# Note that we don't need to write code to calculate the square root,
# which involves many lines of code and a complex algorithm.
# This is because we recognize that num is a number data type, and
# Python already provides the square root function for numbers.
square_root = math.sqrt(num)

# Now we take the square root and square it, which mathematically
# should result in the exact original num value:
print("The square is", square_root ** 2)

Output?

The square is 2.0000000000000004

We see that the output is not exactly the same as the original num value. However, since num has a precision of one digit after the decimal point, if we also consider only one digit after the decimal point for the output, then the output exactly matches num.

Common Functions for Numbers

Python has many useful functions for the number data type. We'll cover some of the most common ones here and we'll discuss other functions as we continue further into data science.

# Continuing with the squaring of the square root calculation above,
# Original print statement:
print("The square is", square_root ** 2)

# With rounding to 1 digit after the decimal point:
print("With rounding, the square is", round(square_root ** 2, 1))

Output?

The square is 2.0000000000000004
With rounding, the square is 2.0

num1 = 2.5
num2 = 3
# What's the difference between the 2 numbers?

# Without using the abs function, we could end up with 2 different results,
# depending on how the difference is calculated:
print("The difference is", num1 - num2)
print("The difference is", num2 - num1)

print("\nWith absolute value:")
# But if we use the absolute value of result, then we always get the
# true difference between the 2 numbers:
print("The difference is", abs(num1 - num2))
print("The difference is", abs(num2 - num1))

Output?

The difference is -0.5
The difference is 0.5

With absolute value:
The difference is 0.5
The difference is 0.5

print("The largest value of 1,5,0,-2,4 is", max(1,5,0,-2,4))
print("The smallest value of 1,5,0,-2,4 is", min(1,5,0,-2,4))

Output?

The largest value of 1,5,0,-2,4 is 5
The smallest value of 1,5,0,-2,4 is -2

import math

num = 5
print("The square root of num:", math.sqrt(num))
print("The square root of num:", round(math.sqrt(num),2))

Output?

The square root of num: 2.23606797749979
The square root of num: 2.24

Common Functions for Strings

Just like with numbers, Python provides many useful functions for strings. Here we cover some of the most common ones.

string1 = "Python"
string2 = "Language"

print("Concatenate:", string1 + string2)
print("Concatenate with space in the middle:", string1 + " " + string2)
print("Concatenate with a new string in the middle:", string1 + ' **--** ' + string2)

Output?

# Can you predict the output of this program?

str1 = "hello"
str2 = "good bye"
output_string = str1 + " and " + str2
print(output_string)

Output?

hello and good bye

Relational operators

There are 6 relational operators:

> : greater than
< : less than
>= : greater than or equal to
<= : less than or equal to
== : equal to
!= : not equal to

When Python evaluates a relational expression, the result is the value True or False.

Comparing numbers

Comparing numbers works as expected in math.
Can you predict the output of the following code?

num1 = 5
num2 = 8

print("num1 > num2?", num1 > num2)
print("num1 < num2?", num1 < num2)
print("num1 >= num1 - 1?", num1 >= num1 - 1)
print("num1 <= num1?", num1 <= num1)
print("num1 == num2?", num1 == num2)
print("num1 != num2?", num1 != num2)

Output?

Comparing strings

Strings can also be compared. When two strings are compared:

• They are compared alphabetically.
  The string ab comes before ac or is "less than" ac.
• If the two strings have the same starting characters, but one string has extra characters at the end, then the shorter string comes before the longer string or is "less than" the longer string.
  The string ab comes before abc or is "less than" abc.
• Uppercase letters come before lowercase letters.
  The string ab comes after Ab or is "greater than" Ab.

Can you predict the output of the following code?

num1 > num2? False
num1 < num2? True
num1 >= num1 - 1? True
num1 <= num1? True
num1 == num2? False
num1 != num2? True

Comparing strings

Strings can also be compared. When two strings are compared:

• They are compared alphabetically.
  The string ab comes before ac or is "less than" ac.
• If the two strings have the same starting characters, but one string has extra characters at the end, then the shorter string comes before the longer string or is "less than" the longer string.
  The string ab comes before abc or is "less than" abc.
• Uppercase letters come before lowercase letters.
  The string ab comes after Ab or is "greater than" Ab.

Can you predict the output of the following code?

string1 = "Python"
string2 = "Programming"
string3 = "PYthon"
string4 = "PY"

print("string1 < string2?", string1 < string2)
print("string1 < string3?", string1 < string3)
print("string3 < string4?", string3 < string4)

Output?

string1 < string2? False
string1 < string3? False
string3 < string4? False