Stem & Leaf Plot

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

# Generate realistic exam scores with slight negative skew
np.random.seed(42)
# Create a negatively skewed distribution
scores = np.random.normal(loc=82, scale=10, size=35)
# Apply negative skew transformation
scores = scores - 0.5 * (scores - np.mean(scores))**2 / np.std(scores)
# Clip to range and round
scores = np.clip(scores, 52, 98)
scores = np.round(scores).astype(int)

# Adjust to meet exact requirements
while len(scores) != 35 or np.mean(scores) < 77 or np.mean(scores) > 79 or np.median(scores) < 79 or np.median(scores) > 81:
    scores = np.random.normal(loc=82, scale=10, size=35)
    scores = scores - 0.5 * (scores - np.mean(scores))**2 / np.std(scores)
    scores = np.clip(scores, 52, 98)
    scores = np.round(scores).astype(int)

# Sort scores for stem-and-leaf
scores_sorted = np.sort(scores)

# Create stem-and-leaf plot data
stem_leaf = {}
for score in scores_sorted:
    stem = score // 10
    leaf = score % 10
    if stem not in stem_leaf:
        stem_leaf[stem] = []
    stem_leaf[stem].append(leaf)

# Sort leaves within each stem
for stem in stem_leaf:
    stem_leaf[stem].sort()

# Calculate statistics
n = len(scores)
min_score = np.min(scores)
q1 = np.percentile(scores, 25)
median = np.median(scores)
q3 = np.percentile(scores, 75)
max_score = np.max(scores)
mean_score = np.mean(scores)
std_score = np.std(scores)

# Find mode(s)
unique, counts = np.unique(scores, return_counts=True)
max_count = np.max(counts)
modes = unique[counts == max_count]

# Create the plot
fig, ax = plt.subplots(figsize=(12, 10))
ax.set_xlim(-10, 10)
ax.set_ylim(-10, 10)
ax.axis('off')

# Title
plt.text(0, 9, 'Statistics 101 Final Exam Score Distribution', 
         fontsize=16, fontweight='bold', ha='center')

# Stem-and-leaf plot
y_pos = 7
plt.text(-8, y_pos, 'Stem-and-Leaf Plot:', fontsize=12, fontweight='bold')

y_pos -= 0.8
for stem in sorted(stem_leaf.keys()):
    leaves_str = ' '.join([str(leaf) for leaf in stem_leaf[stem]])
    plt.text(-6, y_pos, f'{stem} | {leaves_str}', fontsize=11, family='monospace')
    y_pos -= 0.6

# Key
y_pos -= 0.5
plt.text(-6, y_pos, 'Key: 7 | 5 = 75', fontsize=10, style='italic')

# Mark passing grade (70)
y_pos -= 1.5
plt.text(-8, y_pos, 'Passing Grade (70):', fontsize=11, fontweight='bold')
y_pos -= 0.6
plt.text(-6, y_pos, '← Students below this score need remediation', fontsize=10)

# Highlight mode(s)
y_pos -= 1.2
plt.text(-8, y_pos, f'Mode(s): {", ".join(map(str, modes))} (appears {max_count} times)', 
         fontsize=11, fontweight='bold', color='red')

# Summary statistics
y_pos -= 1.5
plt.text(-8, y_pos, 'Summary Statistics:', fontsize=12, fontweight='bold')

stats_text = [
    f'n = {n}',
    f'Min = {min_score}',
    f'Q1 = {q1:.1f}',
    f'Median = {median:.1f}',
    f'Q3 = {q3:.1f}',
    f'Max = {max_score}',
    f'Mean = {mean_score:.1f}',
    f'SD = {std_score:.1f}'
]

y_pos -= 0.8
for stat in stats_text:
    plt.text(-6, y_pos, stat, fontsize=10)
    y_pos -= 0.5

# Distribution shape comparison
y_pos -= 0.8
plt.text(-8, y_pos, 'Distribution Shape:', fontsize=11, fontweight='bold')
y_pos -= 0.6
skewness = stats.skew(scores)
if skewness < -0.5:
    shape = 'Negatively skewed (left tail)'
elif skewness > 0.5:
    shape = 'Positively skewed (right tail)'
else:
    shape = 'Approximately normal'
plt.text(-6, y_pos, f'{shape} (skewness = {skewness:.2f})', fontsize=10)

# Add a simple histogram representation on the right
ax2 = fig.add_axes([0.55, 0.15, 0.35, 0.35])
ax2.hist(scores, bins=15, edgecolor='black', alpha=0.7, color='skyblue')
ax2.axvline(x=70, color='red', linestyle='--', linewidth=2, label='Passing Grade')
ax2.set_xlabel('Score', fontsize=10)
ax2.set_ylabel('Frequency', fontsize=10)
ax2.set_title('Score Distribution', fontsize=11)
ax2.legend(fontsize=9)
ax2.grid(True, alpha=0.3)

plt.tight_layout()


plt.savefig('exam_scores_analysis.png', dpi=300, bbox_inches='tight')
plt.show()
# END-OF-CODE

5 | 2 2 7 8
7 | 1 1 3 6 6 6 7 8 8 8 9
8 | 0 0 0 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5
Key: 7 | 5 = 75
n = 35, Median = 80.0, Mode = 84 (appears 5 times)