Median Calculator

Question

This is just a simple median calculator that calculates the median for a given array/list.

def median(lst):
 nl = []
 nl = sorted(lst)
 e = int(len(nl))
 if e % 2 != 0: # True if odd # of #'s
 ind = int(((e / 2.0) - 0.5)) # index of the median
 c = nl[ind]
 print c
 else: # even # of #'s
 ind_left = int(e / 2.0) - 1 # index left of median
 ind_right = int(e / 2.0) # index right of median
 z = (nl[ind_left] + nl[ind_right]) / 2.0
 print z
median([4, 4, 5, 5, 2.5])

Answer 1

Please name your variables appropriately. Single-letter variables are in most cases sub-optimal and make it needlessly hard for the you-in-six-weeks to figure out what it does.

I'm fairly sure your algorithm is sub-par as well, although I'm not that proficient in algorithms myself. I suspect a function like this already exists in the Python library, I'll update this answer when I've found it.

The following is double work:

nl = []
nl = sorted(lst)

The following will suffice:

nl = sorted(lst)

If you'd be using Python 3.4 or higher, statistics.median would solve your problem.

In Python 2.7 you'll have to install NumPy, an often used library for large number calculations. Now use numpy.median like this:

import numpy as np
def median(lst):
 return np.median(np.array(lst))
print(median([4, 4, 5, 5, 2.5]))

Python usually has basic functions like this already available to you. If it's already available in commonly used Python libraries, it's usually a good idea not to re-invent the wheel yourself.

• Konrad Rudolph: You’re right, the algorithm is sub-par. In fact, a partial sorting of the lower half of the list is sufficient., since we don’t care about the remainder of the list. In fact, we only care about the correct positioning of the one (or two) elements in the middle, but to achieve this we need to sort the lower half.

Answer 2

1. Like @Mast mentioned already mentioned you should use proper variable named in your program. A good variable name makes the program so much easier to read, specially if you're reading it after couple of months.

   There are only two hard things in Computer Science: cache invalidation and naming things. — Phil Karlton

2. e = int(len(nl))

   The call to int() is redundant, length is always an integer.

3. Given integer operands you can get floored division in both Python 2 and 3 using // operator. This prevents the int() conversions as we are not dealing with floats here.

4. Return your result instead of printing it. That way you can import this function in other modules as well, making it re-usable.

New version of your program:

def median(seq):
 new_list = sorted(seq)
 length = len(seq)
 if length % 2 != 0:
 index = length // 2
 median = new_list[index]
 else:
 index_right = length // 2
 index_left = index_right - 1
 median = (new_list[index_left] + new_list[index_right]) / 2.0
 return median

• Grajdeanu Alex: I was getting bored so I did a beautiful one-liner from your function: def median(seq): return sorted(seq)[len(seq) // 2] if len(seq) % 2 != 0 else (sorted(seq)[len(seq) // 2 - 1] + sorted(seq)[len(seq) // 2]) / 2.0

Answer 3

If you're willing to upgrade to Python 3 you can do this with statistics.median. I'd recommend that you upgrade. And would make your code:

from statistics import median
print(median([4, 4, 5, 5, 2.5]))

---

As for your code:

• You don't need to create a list nl to assign a new list to it.
• You don't need to int(len()), it's an int already.
• It's easier to understand e % 2 == 1 over e % 2 != 0.
• You can just floor divide if the list is even or odd, this can be done with //.
• You don't need to assign to variables if you can readably return.
• You don't need a variable to index both the left and right of the center of the list.
• Keep your numbers as integers, don't use 2.0 or float. This removes the need to int.
• Don't print, return.
• n would be a better single variable name rater than e.
• i would also be an easy to read variable name instead of ind_right. Which is good as you use it twice.
• nl is strange at best, d or data are better variable names.
• You don't error if the size of the input array is 0. Instead raise a ValueError.

This can get you:

def median(data):
 data = sorted(data)
 n = len(data)
 if n == 0:
 raise ValueError("no median for empty data")
 if n%2 == 0:
 return data[n//2]
 else:
 i = n//2
 return (data[i - 1] + data[i]) / 2.0

Answer 4

Your variable naming really needs improvements. 1 simple rule I usually follow: if you have trouble finding a good name for a variable, then you don't need it (e, z, c, ind, ).

def median(elements):
 sorted_elements = sorted(elements)
 div, mod = divmod(len(elements), 2)
 return (sorted_elements[div+mod-1] + sorted_elements[div]) / 2
assert median([1, 2, 3]) == 2
assert median([1, 2, 3, 4]) == 2.5
assert median([4, 4, 5, 5, 2.5, 1]) == 4
assert median([4, 4, 5, 5, 2.5, 1, 6]) == 4

• Peilonrayz: Your code doesn't work with median([1, 2, 3]) -> 2.5 and median([1, 2, 3, 4]) -> 3.
• Guillaume: @Peilonrayz: you are right, I fixed it (hopefully)
• Peilonrayz: Looks correct. It was a one-off error, and so you could have just added, -1 to the second index, ;P return (sorted_elements[div] + sorted_elements[div+mod-1]) / 2
• Guillaume: Right once again :) And that is actually what I wanted to do from the beginning :p

Answer 5

Apart from what @Mast already said, here is another small suggestion regarding your actual code:

e = int(len(nl))

The above is always going to be an int as you can't have a float number of items in a list. So:

e = len(nl) 

will do as well.

• Mast: Good catch, I hadn't realized yet there was a useless cast going on.

Answer 6

I am assuming that you want to keep this function general, or that you are intentionally re-inventing the wheel (otherwise you would likely want to use numpy's median function, or the statistics median function for python 3.4+).

First:

def median(lst):

I don't see any length checking on the list. If the user supplies an empty list, I would expect a meaningful exception.

Alternatively, the function could provide an optional default value (similar to the built-in sum), but this would be less intuitive to me.

Second:

 nl = []
 nl = sorted(lst)
 e = int(len(nl))

Initializing n1 is unnecessary here. The result of len also does not need to be converted - the result is always an int. The variable names should also be more descriptive to explain their contents or intent.

Third:

 if e % 2 != 0: # True if odd # of #'s
 ind = int(((e / 2.0) - 0.5)) # index of the median
 c = nl[ind]
 print c

In any language, I am always very careful when doing rounding and/or floating point operations. The correctness of this looks questionable to me (especially without comments). Luckily, python has integer division (//), which rounds down and makes simpler operations like this one clearer.

This could should also return the value, rather than printing it, in order to keep the IO portions separate from the calculations. Separating the print will make it easier to maintain and re-use the function.

Fourth:

 else: # even # of #'s
 ind_left = int(e / 2.0) - 1 # index left of median
 ind_right = int(e / 2.0) # index right of median
 z = (nl[ind_left] + nl[ind_right]) / 2.0
 print z

An obvious optimization here is to avoid recalculating the value in ind_left to get ind_right (ind_left == ind_right - 1).

Taking all of these suggestions will result in code that is something like this:

def median(lst):
 if not lst:
 raise ValueError('Cannot find median of an empty list')
 sorted_items = sorted(lst)
 # Determine if even number of items (True) or odd (False)
 is_even = (len(sorted_items) % 2) == 0
 median_index_l = len(sorted_items) // 2
 if is_even:
 # Even number of items -- median is average of two middle items
 return (sorted_items[median_index_l] + sorted_items[median_index_l + 1]) / 2.0
 else:
 # Odd number of items -- median is middle item
 return sorted_items[median_index_l]

• Oscar Smith: Since you only use is_even once, why not just write if lem(sorted_items) % 2:?
• Casey Kuball: @OscarSmith For readability. If I wanted to optimize it, I could use one of the two library functions, write it in C, etc.
• Casey Kuball: In retrospect looking back at this, I can see a default return of None for an empty list being acceptable (though it's passing an error downstream - not recommended).