Central Tendency — Mean, Median and Mode

import pandas as pd

# Weekly order values for an e-commerce store — 10 orders this week
orders_df = pd.DataFrame({
    'order_id':    [3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 3010],
    'customer':    ['Alice', 'Bob', 'Carol', 'Dave', 'Eve', 'Frank', 'Grace', 'Hank', 'Ivy', 'Jack'],
    'order_value': [45.00, 120.00, 89.00, 34.00, 210.00, 67.00, 95.00, 52.00, 78.00, 110.00]
})

# .mean() calculates the arithmetic average — sum of all values divided by count
mean_order = orders_df['order_value'].mean()
print(f"Mean order value: ${mean_order:.2f}")

# Show what's happening under the hood — .mean() is just sum / count
total  = orders_df['order_value'].sum()    # add up every order value
count  = orders_df['order_value'].count()  # how many orders exist
manual = total / count                     # this is literally what .mean() computes

print(f"\nTotal revenue   : ${total:.2f}")
print(f"Number of orders: {count}")
print(f"Manual mean     : ${manual:.2f}")  # same answer — no magic

import pandas as pd

# Same orders — but MegaCorp places a huge $4,500 bulk order this week
orders_with_outlier = pd.DataFrame({
    'order_id':    [3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 3010, 3011],
    'customer':    ['Alice', 'Bob', 'Carol', 'Dave', 'Eve', 'Frank', 'Grace', 'Hank', 'Ivy', 'Jack', 'MegaCorp'],
    'order_value': [45.00, 120.00, 89.00, 34.00, 210.00, 67.00, 95.00, 52.00, 78.00, 110.00, 4500.00]
})

# Calculate mean with the outlier included
mean_val   = orders_with_outlier['order_value'].mean()

# Calculate median — the middle value, much less sensitive to outliers
median_val = orders_with_outlier['order_value'].median()

print(f"Mean order value  : ${mean_val:.2f}")
print(f"Median order value: ${median_val:.2f}")
print(f"\nDifference        : ${mean_val - median_val:.2f}")
print("\nThe mean jumped from $90 to $491 because of one order.")
print("The median barely moved — it's still near the original data.")

import pandas as pd

# House prices in a neighbourhood — mostly modest homes, two luxury outliers
housing_df = pd.DataFrame({
    'property_id': [501, 502, 503, 504, 505, 506, 507, 508, 509, 510],
    'address':     ['12 Oak St', '45 Pine Ave', '8 Elm Rd', '33 Maple Dr', '19 Birch Ln',
                    '72 Cedar Ct', '5 Willow Way', '88 Ash Blvd', '61 Walnut Pl', '14 Spruce Rd'],
    'price':       [280000, 315000, 295000, 340000, 260000,
                    310000, 275000, 1850000, 290000, 2400000]  # last two are luxury mansions
})

# Sort prices so you can see the distribution clearly
print("Sorted prices:", sorted(housing_df['price'].tolist()))

# .median() sorts all values and returns the middle one
mean_price   = housing_df['price'].mean()
median_price = housing_df['price'].median()

print(f"\nMean house price  : ${mean_price:,.0f}")
print(f"Median house price: ${median_price:,.0f}")
print(f"\nA typical buyer should expect to pay around ${median_price:,.0f}")
print(f"The mean of ${mean_price:,.0f} is misleading — pulled up by two mansions.")

import pandas as pd

# T-shirt orders for the past two weeks — each row is one order
tshirt_df = pd.DataFrame({
    'order_id': range(4001, 4021),   # 20 orders
    'size':     ['M', 'L', 'M', 'XL', 'S', 'M', 'L', 'M', 'S', 'M',
                 'L', 'M', 'XL', 'M', 'L', 'S', 'M', 'M', 'L', 'XL'],
    'colour':   ['Black', 'White', 'Black', 'Blue', 'Black', 'White', 'Black', 'Blue', 'Black', 'White',
                 'Black', 'Black', 'White', 'Black', 'Blue', 'Black', 'White', 'Black', 'Blue', 'Black']
})

# .mode() returns the most frequently occurring value(s)
# It returns a Series — use [0] to get the top result
most_common_size   = tshirt_df['size'].mode()[0]
most_common_colour = tshirt_df['colour'].mode()[0]

print(f"Most ordered size  : {most_common_size}")
print(f"Most ordered colour: {most_common_colour}")

# .value_counts() shows full frequency table — great companion to mode
print("\nSize breakdown:")
print(tshirt_df['size'].value_counts())

print("\nColour breakdown:")
print(tshirt_df['colour'].value_counts())

import pandas as pd

# Gym member ages — realistic distribution with a few older long-term members
gym_df = pd.DataFrame({
    'member_id': range(5001, 5021),   # 20 members
    'name': ['Alex', 'Bella', 'Carlos', 'Diana', 'Ethan', 'Fiona', 'George', 'Hana',
             'Ivan', 'Julia', 'Kevin', 'Laura', 'Mike', 'Nina', 'Oscar', 'Petra',
             'Quinn', 'Rosa', 'Sam', 'Tina'],
    'age': [24, 28, 22, 31, 26, 29, 24, 35, 27, 24,
            33, 28, 62, 25, 29, 31, 24, 27, 58, 30],
    'membership': ['Monthly', 'Annual', 'Monthly', 'Annual', 'Monthly', 'Annual', 'Monthly', 'Annual',
                   'Monthly', 'Monthly', 'Annual', 'Monthly', 'Annual', 'Monthly', 'Monthly', 'Annual',
                   'Monthly', 'Monthly', 'Annual', 'Monthly']
})

# Calculate all three central tendency measures for age
mean_age   = gym_df['age'].mean().round(1)    # arithmetic average
median_age = gym_df['age'].median()            # middle value when sorted
mode_age   = gym_df['age'].mode()[0]           # most frequently occurring age

print(f"Mean age  : {mean_age}")
print(f"Median age: {median_age}")
print(f"Mode age  : {mode_age}")

# The gap between mean and median signals skew
gap = mean_age - median_age
print(f"\nMean - Median gap: {gap}")
if gap > 2:
    print("Positive gap → distribution is right-skewed (a few older members pulling mean up)")
elif gap < -2:
    print("Negative gap → distribution is left-skewed")
else:
    print("Small gap → distribution is roughly symmetric")

# Most common membership type — mode on a categorical column
print(f"\nMost common membership: {gym_df['membership'].mode()[0]}")