1. Simple stats
THe statistics module is part of the python standard library.
1.1. Mean
The mean of a list can be found using the sum and len functions.
The average is found by dividing the sum by len of the list.
mylist = [17, 13, 14, 16, 12, 12]
mymean = sum(mylist)/len(mylist)
print("Mean:", mymean)
# 14.0
Alternatively, the mean of a list can be found using statistics.mean(list).
from statistics import mean
mylist = [17, 13, 14, 16, 12, 12]
mymean = mean(mylist)
print("Mean usings statistics module:", mymean)
# 14
The mean above is 14.
1.2. Sort list
The list of numbers can be sorted in ascending order using mylist.sort().
This is useful for manually checking for the median and mode.
mylist = [17, 13, 14, 16, 12, 12]
mylist.sort()
print("Sorted list:", mylist)
# [12, 12, 13, 14, 16, 17]
The sorted list is: [12, 12, 13, 14, 16, 17]
1.3. Median
For the median, the middle value is returned if there is an odd number of numbers in the list.
The average of the two middle values is returned if there is an even number of numbers in the list.
mylist = [17, 13, 14, 16, 12, 12]
mylist.sort()
n = len(mylist)
if n % 2 == 0:
# average of middle 2 for even number of numbers
mymedian = (mylist[n//2 - 1] + mylist[n//2]) / 2
else:
# middle number of odd number of numbers
mymedian = mylist[n//2]
print("Median:", mymedian)
# 13.5
mylist.sort() sorts the list in ascending order.
n = len(mylist) calculates the length of the list mylist using the len function and stores the result in a variable n.
if n % 2 == 0: checks if n is even by calculating the remainder of n divided by 2 using the modulo operator %. If the remainder is 0, this means that n is even.
mymedian = (mylist[n//2 - 1] + mylist[n//2]) / 2 calculate the median of the list mylist as the average of the two middle elements, if n is even. The two middle elements are accessed using indexing with the expression n//2 - 1 and n//2. n//2 performs integer division (also known as floor division). The result of the division is rounded down to the nearest integer. The average is calculated by adding these two elements and dividing by 2. The result is stored in a variable mymedian.
mymedian = mylist[n//2] calculate the median of the list mylist as the middle element if n is odd. The middle element is accessed using indexing with the expression n//2. The result is stored in a variable mymedian.
It’s important to note that this code assumes that the list mylist is already sorted in ascending order.
Alternatively, the median of a list can be found using statistics.median(list).
from statistics import median
mylist = [17, 13, 14, 16, 12, 12]
mymedian = median(mylist)
print("Median usings statistics module:", mymedian)
# 13.5
The mean above is 13.5.
1.4. Mode
The mode can be found by first creating a dictionary that counts the number of occurances of each number.
mylist = [17, 13, 14, 16, 12, 12]
# Count the occurrences of each number
num_counts = {}
for num in mylist:
if num in num_counts:
num_counts[num] += 1
else:
num_counts[num] = 1
# Print the frequency of each number
for num, cnt in num_counts.items():
print(f"{num}: {cnt}")
# Find the number with the highest count
mode_count = max(num_counts.values())
mode_num = [num for num, cnt in num_counts.items() if cnt == mode_count]
print("Mode:", mode_num)
# [12]
Below is the output showing the frequencies of each number.
Table of counts:
12: 2
13: 1
14: 1
16: 1
17: 1
Here’s an explanation of how each line in the given Python code works:
mylist = [17, 13, 14, 16, 12, 12] defines a list mylist with the given elements.
num_counts = {} defines an empty dictionary num_counts that will be used to store the number of occurrences of each number in the list mylist.
for num in mylist: starts a for loop that iterates over each element num in the list mylist.
if num in num_counts: checks if num is already a key in the dictionary num_counts.
num_counts[num] += 1 increments the value associated with this key by 1 if num is already a key in the dictionary.
num_counts[num] = 1 adds a new key-value pair to the dictionary with key num and value 1 if num is not already a key in the dictionary.
for num, cnt in num_counts.items(): starts another for loop that iterates over each key-value pair (num, cnt) in the dictionary num_counts. The variable num takes on the value of each key and the variable cnt takes on the value of each value.
print(f”{num}: {cnt}”) prints the current key-value pair (num, cnt) to the console.
mode_count = max(num_counts.values()) uses the max function to find the maximum value in the dictionary num_counts. This maximum value is stored in a variable mode_count.
mode_num = [num for num, cnt in num_counts.items() if cnt == mode_count] uses a list comprehension to create a list mode_num of all keys (i.e., numbers) in the dictionary that have a value equal to mode_count. In other words, this list contains all numbers that have the highest count.
print(“Mode:”, mode_num) prints the list mode_num to the console.
Alternatively, the mode of a list can be found using statistics.multimode(list).
This returns a list of modes.
A list is returned even if there is just a single mode.
from statistics import multimode
mylist = [17, 13, 14, 16, 12, 12]
mymode = multimode(mylist)
print("Mode:", mymode)
# [12]
1.5. Range
The range can be found using the max and min values.
mylist = [17, 13, 14, 16, 12, 12]
myrange = max(mylist) - min(mylist)
print(myrange)
# 5