Percentiles for Business Context

Report key percentiles to tell a richer story than mean alone:

p1:   Bottom 1% (floor / minimum typical value)
p5:   Low end of normal range
p25:  First quartile
p50:  Median (typical user)
p75:  Third quartile
p90:  Top 10% / power users
p95:  High end of normal range
p99:  Top 1% / extreme users

Example narrative: "The median session duration is 4.2 minutes, but the top 10% of users spend over 22 minutes per session, pulling the mean up to 7.8 minutes."

Describing Distributions

Characterize every numeric distribution you analyze:

• Shape: Normal, right-skewed, left-skewed, bimodal, uniform, heavy-tailed
• Center: Mean and median (and the gap between them)
• Spread: Standard deviation or IQR
• Outliers: How many and how extreme
• Bounds: Is there a natural floor (zero) or ceiling (100%)?

Trend Analysis and Forecasting

Identifying Trends

Moving averages to smooth noise:

# 7-day moving average (good for daily data with weekly seasonality)
df['ma_7d'] = df['metric'].rolling(window=7, min_periods=1).mean()

# 28-day moving average (smooths weekly AND monthly patterns)
df['ma_28d'] = df['metric'].rolling(window=28, min_periods=1).mean()

Period-over-period comparison:

• Week-over-week (WoW): Compare to same day last week
• Month-over-month (MoM): Compare to same month prior
• Year-over-year (YoY): Gold standard for seasonal businesses
• Same-day-last-year: Compare specific calendar day

Growth rates:

Simple growth: (current - previous) / previous
CAGR: (ending / beginning) ^ (1 / years) - 1
Log growth: ln(current / previous)  -- better for volatile series

Seasonality Detection

Check for periodic patterns:

1. Plot the raw time series -- visual inspection first
2. Compute day-of-week averages: is there a clear weekly pattern?
3. Compute month-of-year averages: is there an annual cycle?
4. When comparing periods, always use YoY or same-period comparisons to avoid conflating trend with seasonality

Forecasting (Simple Methods)

For business analysts (not data scientists), use straightforward methods:

• Naive forecast: Tomorrow = today. Use as a baseline.
• Seasonal naive: Tomorrow = same day last week/year.
• Linear trend: Fit a line to historical data. Only for clearly linear trends.
• Moving average forecast: Use trailing average as the forecast.

Always communicate uncertainty. Provide a range, not a point estimate:

• "We expect 10K-12K signups next month based on the 3-month trend"
• NOT "We will get exactly 11,234 signups next month"

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