Python Modules: math, random and statistics

Importing modules and using math (sqrt, ceil, floor, pow, fabs, pi), random (random, randint, randrange) and statistics (mean, median, mode).

Key ideas

import math loads the whole module, so its functions are called as math.sqrt(x); from math import sqrt lets you write sqrt(x).
math.sqrt(), math.pow() and math.fabs() always give floats; math.ceil() and math.floor() give ints.
ceil() rounds up to the next whole number and floor() rounds down, so for a negative number floor() moves away from zero.
random.random() gives a float from 0 up to but not including 1; randint(a, b) includes both a and b; randrange(a, b, c) stops before b.
statistics.mean() adds and divides; median() is the middle of the sorted data (the mean of the two middle values for an even count); mode() is the most frequent value.
mean() of whole numbers prints as an int when it is exact (19) and as a float when not (19.4); a median of an even count is a float.

Remember

math results	math.sqrt(25) = 5.0; math.pow(2, 3) = 8.0 but 2 ** 3 = 8; math.fabs(−7) = 7.0
ceil and floor	math.ceil(4.1) = 5; math.floor(7.9) = 7; math.floor(−2.5) = −3
Constants	math.pi = 3.141592653589793; math.e = 2.718281828459045
random ranges	randint(1, 6): 1 to 6; randrange(0, 10, 2): 0, 2, 4, 6, 8; random(): 0 ≤ x < 1
How many values	randint(a, b) can give b − a + 1 different values
statistics	data [4, 8, 8, 5]: mean 6.25, median 6.5, mode 8
Buses needed	math.ceil(students / seats): 130 students, 40 seats → 4 buses

Watch out

Writing sqrt(16) after import math: it must be math.sqrt(16).
Expecting randint(1, 6) to stop at 5: unlike range(), it includes both ends.
Writing 8 for math.pow(2, 3): it gives 8.0.
Taking the middle of the unsorted data as the median.

Worked example

What does this program print? Give the three lines (a) to (c).
import statistics as st
data = [29, 5, 21, 20, 20]
print(st.mean(data))
print(st.median(data))
print(st.mode(data))

Working: sum 95 ÷ 5; sorted: 5, 20, 20, 21, 29; mean of whole numbers prints without .0 only when it is exact, and the median of an even count is a float

Answer: (a) 19; (b) 20; (c) 20