Essential Statistical Functions for Data Analysis and Decision-Making

Basic Descriptive Statistics

stats$max

When to Use: Finding the peak value in a dataset, such as the highest daily stock price in a month.

• Example: A trader analyzes a stock’s price history in sample->value1 to identify its maximum value over 100 days.
• Returned Value: The highest value (e.g., 100 for sample->value1).
• Decision: If the stats$max is unusually high (e.g., a stock spike), investigate a market event or sell at the peak.

stats$min

When to Use: Identifying the lowest point, such as the minimum temperature in a weather dataset.

• Example: A farmer checks soil sensor readings in sample->value1 to find the lowest moisture level over a season.
• Returned Value: The smallest value (e.g., 1 for sample->value1).
• Decision: If the stats$min is too low (e.g., drought conditions), increase irrigation or adjust crop planning.

stats$range

When to Use: Measuring the spread between highest and lowest values, such as temperature fluctuation.

• Example: A meteorologist analyzes 100 daily temps in sample->value1.
• Returned Value: Range (e.g., 99 for sample->value1).
• Decision: If stats$range is wide (e.g., 99 vs. avg 20), prepare for extreme weather conditions.

stats$sum

When to Use: Aggregating totals, such as total sales revenue over a period.

• Example: A retailer sums daily sales in sample->value1 across 100 stores.
• Returned Value: The total (e.g., 5050 for sample->value1).
• Decision: If the stats$sum exceeds targets (e.g., $5050 vs. $5000 goal), allocate bonuses or expand inventory.

stats$mean

When to Use: Measuring central tendency, such as average customer wait time in a call center.

• Example: A manager evaluates 100 call durations in sample->value1.
• Returned Value: The arithmetic mean (e.g., 50.5 for sample->value1).
• Decision: If the stats$mean is high (e.g., 50.5 minutes vs. 30-minute target), hire more staff or streamline processes.

stats$median

When to Use: Robust central tendency, such as median home prices.

• Example: A realtor analyzes 100 sales in sample->value1.
• Returned Value: Middle value (e.g., 50.5 for sample->value1).
• Decision: If stats$median lags market (e.g., $200K vs. $250K), adjust pricing strategies.

stats$mode

When to Use: Most common value, such as popular product size.

• Example: A retailer analyzes 100 shoe sales in sample->value1.
• Returned Value: Mode (e.g., 1 for sample->value1, first unique).
• Decision: If stats$mode is size 8, stock more of that size.

stats$midrange

When to Use: Simple central estimate, like average of extremes in test scores.

• Example: A teacher analyzes 100 scores in sample->value1.
• Returned Value: Midrange (e.g., 50.5 for sample->value1).
• Decision: If stats$midrange deviates from mean (e.g., 50.5 vs. 60), check for skewed data.

Dispersion & Distribution Metrics

stats$stddev

When to Use: Assessing variability, such as consistency of product weights in manufacturing.

• Example: A factory tests 100 widget weights in sample->value1.
• Returned Value: Standard deviation (e.g., ~29.01 for sample->value1).
• Decision: If stats$stddev is high (e.g., 29 vs. target 5), tighten quality control to reduce variation.

stats$var

When to Use: Quantifying spread, such as volatility of investment returns.

• Example: A portfolio manager analyzes 100 daily returns in sample->value1.
• Returned Value: Variance (e.g., ~841.67 for sample->value1).
• Decision: If stats$var is excessive (e.g., 841 vs. 100 benchmark), diversify investments to lower risk.

stats$iqr

When to Use: Measuring middle 50% spread, such as income variability.

• Example: A researcher analyzes 100 incomes in sample->value1.
• Returned Value: IQR (e.g., 49.5 for sample->value1).
• Decision: If stats$iqr is large (e.g., 50 vs. 20 norm), address income inequality or outliers.

stats$cv

When to Use: Relative variability, such as comparing consistency across datasets.

• Example: A quality analyst compares 100 measurements in sample->value1.
• Returned Value: Coefficient of variation (e.g., ~0.575 for sample->value1).
• Decision: If stats$cv is high (e.g., 57% vs. 10% target), improve process stability.

Percentiles & Risk Measures

stats$percentile(50)

When to Use: Finding a specific quantile, such as median income in a survey.

• Example: A sociologist studies 100 household incomes in sample->value1.
• Returned Value: 50th percentile (e.g., 50.5 for sample->value1).
• Decision: If stats$percentile(50) is low (e.g., $50K vs. $60K norm), advocate for wage increases.

stats$zscore(50)

When to Use: Standardizing data, such as identifying outliers in test scores.

• Example: A researcher checks a score of 50 in sample->value1 (100 results).
• Returned Value: Z-score (e.g., -0.0172 for sample->value1).
• Decision: If stats$zscore is extreme (e.g., > 3), flag as an outlier for review.

stats$drawdown

When to Use: Measuring peak-to-trough decline, such as maximum loss in a trading account.

• Example: A trader tracks portfolio value in sample->value1 over 100 days.
• Returned Value: Max drawdown (e.g., 0 for sample->value1 since it’s increasing).
• Decision: If stats$drawdown is high (e.g., 50% in a real portfolio), adjust risk management (e.g., stop-loss orders).

stats$vrisk(0.95)

When to Use: Risk assessment, such as Value at Risk for portfolio losses.

• Example: A fund manager assesses 100 daily returns in sample->value1.
• Returned Value: 95% VaR (e.g., 6 for sample->value1).
• Decision: If stats$vrisk is high (e.g., -10% loss), reduce exposure or hedge positions.

stats$cvrisk(0.95)

When to Use: Expected shortfall, such as average loss beyond VaR in finance.

• Example: Same fund manager as above, using sample->value1.
• Returned Value: CVaR (e.g., 3 for sample->value1).
• Decision: If stats$cvrisk is severe (e.g., -15%), increase cash reserves or diversify.

Skewness & Kurtosis (Shape of Distribution)

stats$skew

When to Use: Checking distribution symmetry, such as customer purchase amounts.

• Example: An e-commerce analyst studies 100 transactions in sample->value1.
• Returned Value: Skewness (e.g., 0 for sample->value1, uniform).
• Decision: If stats$skew is positive (e.g., 2, many small purchases, few large), target high-spenders with promotions.

stats$kurtosis

When to Use: Evaluating tail heaviness, such as risk of extreme events in insurance claims.

• Example: An insurer analyzes 100 claim sizes in sample->value1.
• Returned Value: Excess kurtosis (e.g., -1.236 for sample->value1).
• Decision: If stats$kurtosis is high (e.g., 3, heavy tails), reserve more capital for rare, large claims.

Alternative Measures of Central Tendency

stats$gmean

When to Use: Growth rates, such as average investment return over time.

• Example: An investor tracks 100 daily returns in sample->value1.
• Returned Value: Geometric mean (e.g., ~37.99 for sample->value1).
• Decision: If stats$gmean is low (e.g., 2% vs. 5% target), reassess investment strategy.

stats$hmean

When to Use: Rates or averages with inverses, such as average speed over distances.

• Example: A logistics firm measures 100 delivery speeds in sample->value1.
• Returned Value: Harmonic mean (e.g., ~19.28 for sample->value1).
• Decision: If stats$hmean is slow (e.g., 20 mph vs. 30 mph goal), optimize routes.

Statistical Tests & Inference

stats$ttest

When to Use: Comparing means, such as A/B testing website conversion rates.

• Example: A marketer tests two ad campaigns (sample->value1 vs. sample->value2, 100 clicks each).
• Returned Value: t-statistic (e.g., 0 for sample->value1 vs. sample->value2, equal means).
• Decision: If stats$ttest t-value is significant (e.g., > 2), choose the better campaign; if near 0, no preference.

stats$chi2

When to Use: Goodness-of-fit, such as testing observed vs. expected frequencies.

• Example: A biologist compares 100 observed gene frequencies in sample->value1 vs. expected in sample->value2.
• Returned Value: Chi-squared statistic (e.g., 32,716.438057 or 333,300 with real).
• Decision: If stats$chi2 is high (e.g., > critical value), reject the null hypothesis (data doesn’t fit expected distribution).

stats$ftest

When to Use: Variance comparison, such as consistency of two machines.

• Example: A factory tests output variance from two lines (sample->value1 vs. sample->value2, 100 units each).
• Returned Value: F-statistic (e.g., 1 for sample->value1 vs. sample->value2).
• Decision: If stats$ftest F is significant (e.g., > 1.5), one machine is less consistent—repair or replace.

Regression & Correlation

stats$linreg

When to Use: Linear relationship, such as sales vs. ad spend.

• Example: A marketer correlates 100 days of spend (sample->value1) and sales (sample->value2).
• Returned Value: Slope (e.g., -1 for sample->value1 vs. sample->value2).
• Decision: If stats$linreg slope is positive and steep (e.g., 2), increase ad budget.

stats$pcorr

When to Use: Normalized correlation, such as temperature vs. ice cream sales.

• Example: A vendor analyzes 100 days of data (sample->value1 vs. sample->value2).
• Returned Value: Pearson correlation (e.g., -1 for sample->value1 vs. sample->value2).
• Decision: If stats$pcorr is high positive (e.g., 0.9), stock more ice cream on hot days.

stats$spearman

When to Use: Rank correlation, such as student test scores vs. study hours.

• Example: A teacher compares 100 students’ ranks in sample->value1 vs. sample->value2.
• Returned Value: Spearman’s rho (e.g., -1 for sample->value1 vs. sample->value2).
• Decision: If stats$spearman rho is high (e.g., 0.8), study hours strongly predict scores—encourage study time.

stats$cov

When to Use: Relationship strength, such as stock price correlations.

• Example: A trader compares two stocks over 100 days (sample->value1 vs. sample->value2).
• Returned Value: Covariance (e.g., -841.67 for sample->value1 vs. sample->value2).
• Decision: If stats$cov is negative (e.g., -841), diversify with inversely related assets.

Finance & Risk Analysis

stats$sharpe(0)

When to Use: Risk-adjusted return, such as portfolio performance.

• Example: An investor evaluates 100 daily returns in sample->value1.
• Returned Value: Sharpe ratio (e.g., ~1.74 for sample->value1).
• Decision: If stats$sharpe is low (e.g., < 1), shift to less volatile assets.

stats$cagr

When to Use: Compound growth, such as investment growth rate.

• Example: A financial analyst tracks a fund over 2 years in sample->value1 (100 periods).
• Returned Value: CAGR (e.g., 9 for sample->value1 with num_years = 2).
• Decision: If stats$cagr is strong (e.g., 9% vs. 5% benchmark), recommend the fund.