The code

Straight from labs/course-4-stats/python/02_descriptive_stats.py, unchanged.

"""Course 4 Lab, experiments 3-6: measures of central tendency and dispersion,
histograms and bar charts.

Standard library only -- `statistics` is part of Python, no install needed.
Charts are drawn as text so they render anywhere.
"""

import statistics
from collections import Counter

marks = [45, 67, 78, 52, 89, 91, 73, 64, 58, 82,
         76, 69, 71, 85, 60, 55, 93, 48, 79, 66]

# Step 1: Experiment 3: the mean
print("=" * 62)
print("EXPERIMENT 3: Measures of central tendency")
print("=" * 62)
print(f"Dataset (n = {len(marks)}): {sorted(marks)}\n")

n = len(marks)
mean = sum(marks) / n
ordered = sorted(marks)
if n % 2 == 0:
    median = (ordered[n // 2 - 1] + ordered[n // 2]) / 2
else:
    median = ordered[n // 2]

counts = Counter(marks)
top = max(counts.values())
modes = [v for v, c in counts.items() if c == top]

print("MEAN -- the balance point. Add everything, divide by how many.")
print(f"  mean = {sum(marks)} / {n} = {mean:.2f}")
print(f"  cross-check statistics.mean() = {statistics.mean(marks):.2f}")

# Step 2: The median
print("\nMEDIAN -- the middle value once sorted. Half are below, half above.")
print(f"  n = {n} is even, so average the {n//2}th and {n//2+1}th values:")
print(f"  ({ordered[n//2-1]} + {ordered[n//2]}) / 2 = {median}")
print(f"  cross-check statistics.median() = {statistics.median(marks)}")

# Step 3: The mode
print("\nMODE -- the most frequent value.")
if top == 1:
    print("  every value appears once, so there is no mode")
else:
    print(f"  {modes} (appearing {top} times)")

# Step 4: Which one to use
print("\nWHICH ONE TO USE")
print("  The mean uses every value, so one extreme value drags it. Add a")
print("  single mark of 500 to this dataset:")
skewed = marks + [500]
print(f"    mean   {mean:.2f} -> {sum(skewed)/len(skewed):.2f}   moved a lot")
print(f"    median {median} -> {statistics.median(skewed)}   barely moved")
print("  That resistance is why income and house prices are quoted as medians.")

# Step 5: Experiment 4: range and quartiles
print("\n" + "=" * 62)
print("EXPERIMENT 4: Measures of dispersion")
print("=" * 62)

data_range = max(marks) - min(marks)


def quartile(sorted_data, q):
    """Linear-interpolation quartile, matching Excel's QUARTILE.INC."""
    pos = (len(sorted_data) - 1) * q
    lower = int(pos)
    upper = min(lower + 1, len(sorted_data) - 1)
    return sorted_data[lower] + (pos - lower) * (sorted_data[upper] - sorted_data[lower])


q1, q2, q3 = quartile(ordered, 0.25), quartile(ordered, 0.5), quartile(ordered, 0.75)
iqr = q3 - q1

# Population vs sample: the divisor is n for a population, n-1 for a sample.
pop_var = sum((x - mean) ** 2 for x in marks) / n
sam_var = sum((x - mean) ** 2 for x in marks) / (n - 1)

print(f"RANGE = max - min = {max(marks)} - {min(marks)} = {data_range}")
print("  Uses only two values, so a single outlier defines it entirely.")

print(f"\nQUARTILES and IQR")
print(f"  Q1 = {q1:.2f}   Q2 (median) = {q2:.2f}   Q3 = {q3:.2f}")
print(f"  IQR = Q3 - Q1 = {q3:.2f} - {q1:.2f} = {iqr:.2f}")
print("  The IQR is the spread of the middle 50%, so outliers cannot inflate it.")

# Step 6: Variance and standard deviation
print(f"\nVARIANCE -- the mean squared distance from the mean")
print(f"  population variance (divide by n)     = {pop_var:.2f}")
print(f"  sample variance     (divide by n - 1) = {sam_var:.2f}")
print("  Use n-1 when the data is a SAMPLE. Dividing by n underestimates the")
print("  spread, because deviations are measured from the sample's own mean.")
print("  This is Bessel's correction, and choosing wrongly costs marks.")
print(f"  cross-check statistics.pvariance() = {statistics.pvariance(marks):.2f}")
print(f"  cross-check statistics.variance()  = {statistics.variance(marks):.2f}")

print(f"\nSTANDARD DEVIATION -- the square root of the variance")
print(f"  population sd = {pop_var ** 0.5:.2f}")
print(f"  sample sd     = {sam_var ** 0.5:.2f}")
print("  Back in the original units (marks), unlike variance (marks squared).")

# Step 7: Coefficient of variation, and outliers
print(f"\nCOEFFICIENT OF VARIATION -- relative spread, unit-free")
print(f"  CV = sd / mean x 100 = {sam_var ** 0.5 / mean * 100:.2f}%")

print("\nOUTLIER RULE: anything below Q1 - 1.5xIQR or above Q3 + 1.5xIQR")
low_fence, high_fence = q1 - 1.5 * iqr, q3 + 1.5 * iqr
print(f"  fences: [{low_fence:.2f}, {high_fence:.2f}]")
outliers = [x for x in marks if x < low_fence or x > high_fence]
print(f"  outliers: {outliers if outliers else 'none'}")

# Step 8: Experiment 5: the histogram and its shape
print("\n" + "=" * 62)
print("EXPERIMENT 5: Histogram and the shape of the distribution")
print("=" * 62)

bins = [(40, 50), (50, 60), (60, 70), (70, 80), (80, 90), (90, 100)]
print(f"\n{'Class':<12}{'Frequency':<12}Histogram")
for low, high in bins:
    freq = sum(1 for m in marks if low <= m < high)
    print(f"{low}-{high:<8} {freq:<12}{'#' * freq * 3}")

# Pearson's second coefficient of skewness.
skew = 3 * (mean - median) / (sam_var ** 0.5)
print(f"\nSHAPE")
print(f"  mean = {mean:.2f}, median = {median}")
print(f"  Pearson skewness = 3(mean - median)/sd = {skew:.3f}")
if abs(skew) < 0.5:
    shape = "roughly symmetric"
elif skew > 0:
    shape = "positively skewed -- a tail to the right"
else:
    shape = "negatively skewed -- a tail to the left"
print(f"  The distribution is {shape}.")
print("  Rule of thumb: mean > median suggests a right tail; mean < median a")
print("  left tail; mean = median = mode means perfectly symmetric.")

# Step 9: Experiment 6: a bar chart of categories
print("\n" + "=" * 62)
print("EXPERIMENT 6: Bar chart of categorical data")
print("=" * 62)

survey = [("Male", "A"), ("Female", "A"), ("Male", "B"), ("Female", "B"),
          ("Male", "A"), ("Female", "C"), ("Male", "C"), ("Female", "A"),
          ("Male", "B"), ("Female", "B"), ("Male", "A"), ("Female", "A"),
          ("Male", "C"), ("Female", "B"), ("Male", "B")]

sections = sorted({s for _, s in survey})
genders = sorted({g for g, _ in survey})

print(f"\n{'Section':<10}" + "".join(f"{g:>10}" for g in genders) + f"{'Total':>10}")
print("-" * 40)
for section in sections:
    row = [sum(1 for g, s in survey if s == section and g == gender)
           for gender in genders]
    print(f"{section:<10}" + "".join(f"{v:>10}" for v in row) + f"{sum(row):>10}")

print("\nGrouped bar chart")
for section in sections:
    for gender in genders:
        count = sum(1 for g, s in survey if s == section and g == gender)
        print(f"  {section}-{gender:<8} {'|' * count * 4} {count}")

print("\nINTERPRETATION")
print("  A bar chart is for CATEGORIES -- the bars are separated, and their")
print("  order carries no meaning. A histogram is for CONTINUOUS data -- the")
print("  bars touch, because the classes are adjacent intervals. Drawing one")
print("  when the question asks for the other is a common way to lose marks.")

Where this sits

One experiment from the Statistical Foundations for Data Science lab. The rest of them, and the theory behind this one, are on the lab page.