Answer key for HW01: Writing key quantities from descriptive statistics in Python yourself

import numpy as np # for working with arrays of numerical values
import scipy  # for various scientific calculations
import xarray as xr  # for loading data and subsequent analyses

import xarray as xr

# `DATA_PATH` variable was created by the hidden cell just above. 
# Un-hide that cell if you want to see the details.
ds_cp = xr.open_dataset(DATA_PATH)
ds_cp

2 + 3

def add(num1, num2):
    """Add the two numbers."""
    return num1 + num2

add(2, 3)

add(2, 3) == (2 + 3)

def add_array(arr):
    """Sum all elements of the array."""
    sum = 0
    for arr_element in arr:  # Loop over every item in the array `arr`
        sum += arr_element  # Add that item to the running sum
    return sum  # Once the loop has run over all elements, give us ("return") the total sum.

import numpy as np
import xarray as xr
import scipy


def sum(x):
    """Adds the elements in a 1d array"""
    sum = 0
    for y in x:
        sum += y
    return sum


def mean(x):
    """Computes the average of elements in a 1d array using the sum function"""
    return sum(x) / len(x)


def median(x):
    """Computes the median of a 1d array using indexing"""
    len_x = len(x)
    x_sorted = sorted(x)
    is_even = len_x % 2 == 0
    if is_even:
        val1 = x_sorted[len_x // 2 - 1]
        val2 = x_sorted[len_x // 2]
        return 0.5 * (val1 + val2)
    else:
        return x_sorted[len(x) // 2]


def stats_range(x):
    """Computes the range max-min using built in functions"""
    return max(x) - min(x)


def variance(x):
    """Computes the variance with a for loop"""
    x_mean = mean(x)
    total = []
    for x_val in x:
        total.append((x_val - x_mean)**2)
    return sum(total) / len(x)


def stdev(x):
    """Square root of variance"""
    return variance(x) ** (1/2)


def coef_var(x):
    """Ratio of standard deviation to mean"""
    return stdev(x) / mean(x)


def iqr(x):
    """Interquartile range 25 to 75"""
    return np.percentile(x, 75) - np.percentile(x, 25)

# Define the toy array we'll test the functions against.
arr_test = [4.0, 1.0, 10.0, 2.0, 4.]
# Print out its values to make sure you copy/pasted it correctly from the HW.
print(f"Toy dataset is: {arr_test}")

# Start with the first measure to be calculated.
# Describe the measure conceptually in words, and report the answer
# that it should produce when computed on the toy array, which you can
# compute by hand or at most using a simple calculator.
print()  # blank line for easier readability
print("Function #1 is the average: add all elements of the array.")
ans_average = 4.2
print(f"We can add those up without a computer or calculator; the answer is {ans_average}.")

# Now call your function on the toy array, and print out the result.
average_toy = mean(arr_test)
print(f"Calling `mean` on the toy dataset.  Answer: {ans_average}")

# Finally, print out the difference between what you expect the answer to be
# and what the actual function computes (this should be zero or *very* close to it).
diff_average = ans_average - average_toy
print(f"Difference between expected and actual: {diff_average}")
print()  # A blank line at the end of each function makes the output easier to read.

# Then repeat the lines of code starting with the "# Describe ..." comment but
# applied to each of the remaining 4 quantities.

########################################################
print()
print("Function #2 is the median: what is the middle value of the sorted array?.")
ans_median = 4
print(f" The answer is {ans_median}.")

median_toy = median(arr_test)
print(f"Calling `median` on the toy dataset.  Answer: {median_toy}")

diff_median = ans_median - median_toy
print(f"Difference between expected and actual: {diff_median}")
print()

########################################################
print()
print("Function #3 is the range: The largest possible difference between two values in the data set.")
ans_range = 9
print(f"The answer is {ans_range}.")

range_toy = stats_range(arr_test)
print(f"Calling `range` on the toy dataset.  Answer: {range_toy}")

diff_range = ans_range - range_toy
print(f"Difference between expected and actual: {diff_range}")
print()

########################################################
print()
print("Function #4 is the variance: a measure of the spread of the dataset.")
ans_var = 9.76

print(f"The answer is {ans_var :.2f}.")

variance_toy = variance(arr_test)
print(f"Calling `variance` on the toy dataset.  Answer: {variance_toy :.2f}")

diff_var = ans_var - variance_toy
print(f"Difference between expected and actual: {diff_var}")
print()

########################################################
print()
print("Function #5 is the standard deviation: the average square distance of a data point from the mean.")
ans_stdev = ans_var ** 0.5

print(f"The answer is {ans_stdev :.2f}.")

stdev_toy = stdev(arr_test)
print(f"Calling `standard deviation` on the toy dataset.  Answer: {stdev_toy :.2f}")

diff_stdev = ans_stdev - stdev_toy
print(f"Difference between expected and actual: {diff_var}")
print()

########################################################
print()
print("Function #6 is the coefficent of variation : the ratio of the standard deviation to the mean.")
ans_var = 0.7438333024673005
print(f"The answer is {ans_var :.2f}.")

variance_toy = coef_var(arr_test)
print(f"Calling `coef_var` on the toy dataset.  Answer: {variance_toy :.2f}")

diff_var = ans_var - variance_toy
print(f"Difference between expected and actual: {diff_var}")
print()

######################################################
print()
print('Extra Credit 1: IQR')
print()
print("Function #7 is the interquartile range : the difference between the 25th and 75th percentiles.")
ans_var = 2
print(f"The answer (scipy.stats.iqr) is {ans_var :.2f}.")

variance_toy = iqr(arr_test)
print(f"Calling `iqr` on the toy dataset.  Answer: {variance_toy :.2f}")

diff_var = ans_var - variance_toy
print(f"Difference between expected and actual: {diff_var}")
print()

######################################################
avg_t_cp = ds_cp["temp_avg"].values

park_mean = np.mean(avg_t_cp)
park_median = np.median(avg_t_cp)
park_range = np.ptp(avg_t_cp)
park_var = np.var(avg_t_cp)
park_stdev = np.std(avg_t_cp)
park_coef = np.std(avg_t_cp) / np.mean(avg_t_cp)
park_iqr = scipy.stats.iqr(avg_t_cp)

print()
print("Extra Credit 2")
print()
print('Testing functions on central park dataset')
print()
print('#############################################')
print('Function 1: Mean')
print(f"Expected {park_mean :.2f}")
print(f"Homemade function {mean(avg_t_cp) :.2f}")
print(f'Difference {park_mean - mean(avg_t_cp) :.2f}')
print('#############################################')
print('Function 2: Median')
print(f"Expected {park_median :.2f}")
print(f"Homemade function {median(avg_t_cp) :.2f}")
print(f'Difference {park_median - median(avg_t_cp) :.2f}')
print('#############################################')
print('Function 3: Range')
print(f"Expected {park_range :.2f}")
print(f"Homemade function {stats_range(avg_t_cp) :.2f}")
print(f'Difference {park_range - stats_range(avg_t_cp) :.2f}')
print('#############################################')
print('Function 4: Variance')
print(f"Expected {park_var :.2f}")
print(f"Homemade function {variance(avg_t_cp) :.2f}")
print(f'Difference {park_var - variance(avg_t_cp) :.2f}')
print('#############################################')
print('Function 5: Standard Deviation')
print(f"Expected {park_stdev :.2f}")
print(f"Homemade function {stdev(avg_t_cp) :.2f}")
print(f'Difference {park_stdev - stdev(avg_t_cp) :.2f}')
print('#############################################')
print('Function 6: Coefficent of Variation')
print(f"Expected {park_coef :.2f}")
print(f"Homemade function {coef_var(avg_t_cp) :.2f}")
print(f'Difference {park_coef - coef_var(avg_t_cp) :.2f}')
print('#############################################')
print('Function 7: interquartile Range')
print(f"Expected {park_iqr :.2f}")
print(f"Homemade function {iqr(avg_t_cp) :.2f}")
print(f'Difference {park_iqr - iqr(avg_t_cp) :.2f}')