LECTURE 2: DESCRIPTIVE ANALYSIS

It is the type of analysis of data that helps describe, show or summarize data points in a constructive way such that patterns might emerge that fulfill every condition of the data.

Descriptive Analysis

It is a statistical procedures used to summarize, organize, and simplify data. This process should be carried out in such a way that reflects overall findings.

Descriptive Statistics

What are the three Benefits of Descriptive Statistics

Raw data is made more manageable

Raw data is presented in a logical form.

Patterns can be seen from organized data

It is a summary measure that attempts to describe a whole set of data - A.L. Bowley

Measures of central tendency

This is simply the average of a range of numbers

Mean

This is the middle point of a range of numbers

Median

This is the most frequent value/s of a range of numbers.

Mode

It is the degree to which numerical data tend to spread about an average value - Spiegel

variation or dispersion of data

It is a number that measures how far away each number in a set of data is from their mean.

Standard Deviation

What is the variable type application of mean

Interval/Ratio

What is the variable type application of median

Ordinal

What is the variable type application of mode

Nominal

A measure of the asymmetry of the distribution.

• Positive skew (right skew) → tail on the right (mean > median).

• Negative skew (left skew) → tail on the left (mean < median).

• Zero skew → symmetric.

Skewness

______ IS A measure of the “tailedness” of the distribution.

• High (leptokurtic) → heavy tails, more extreme outliers.

• Low (platykurtic) → light tails, fewer outliers.

• Normal distribution has ______ ≈ 3

Kurtosis

The difference between the maximum and minimum values.

Range

• Measures how precisely the sample mean estimates the true population mean.

• Smaller → more confidence that the sample average (e.g., average customer wait time) is close to the true average for all customers.

• Used in business to decide if a sample is large enough for reliable forecasts (e.g., before launching a new product based on a test market).

Standard Error

Definition:
The number of observations in the dataset.

Practical Business Interpretation:

• Represents sample size or total number of transactions, days, products, etc.

• Essential for determining reliability of averages (larger count → more stable estimates).

• Example: “We surveyed 500 customers” – count tells you how much trust to put in the results.

• Used to compute many other statistics (e.g., SEM = SD/√n).

Count

The smallest observed value in the dataset.

Practical Business Interpretation:

• Identifies the worst case (e.g., lowest daily sales, slowest delivery time, fewest customers).

• Used to set safety thresholds (e.g., if minimum cash balance drops near zero, take action).

• Helps detect data entry errors (e.g., negative inventory count).

Minimum

The smallest observed value in the dataset.

Practical Business Interpretation:

• Identifies the worst case (e.g., lowest daily sales, slowest delivery time, fewest customers).

• Used to set safety thresholds (e.g., if minimum cash balance drops near zero, take action).

• Helps detect data entry errors (e.g., negative inventory count).

Minimum

• Less intuitive than SD because it is in squared units (e.g., dollars squared).

• Useful for mathematical calculations (e.g., in ANOVA, regression).

• Business example: Comparing variance of sales across regions helps identify which region’s performance is most inconsistent

Sample Variance

• High _____ → Generally positive: the business earns high revenue on average, or customers spend a lot per transaction. However, a high mean might hide inconsistency if standard deviation is also high.

• Low ______ → Suggests poor overall performance: low average sales, low customer spending, or weak profitability. May indicate need for price increases, better marketing, or cost reduction.

Mean

• High ____ → The sample mean is an unreliable estimate of the true population mean. This often happens with small sample sizes or high variability. In business, this means you cannot confidently trust the average (e.g., a test market average might not predict national performance).

• Low _____→ The sample mean is very precise; you can be confident the true average is close to your calculated mean. Useful for making investment or operational decisions based on sample data.

Standard Error of the Mean (SEM)

• High _____→ The typical (middle) value is high. For revenue, this means at least half of your days/months/customers are generating high numbers, regardless of extremes. Often a better indicator of “typical” health than the mean.

• Low _____→ Half of your observations are low. Even if the mean looks okay due to a few big wins, the median reveals that most of your business is struggling.

Median

High _____ → The most common value is high. For example, if the modal transaction amount is ₱500, most customers spend that much. This is good for predictability. But if the mode is low (e.g., most customers buy the cheapest item), you may need to upsell.

• Low _____→ Most frequent value is low. Suggests that the common behavior is low spending, low traffic, or low profit. Could indicate a market segment that needs a new pricing strategy.

Mode

• High _____→ High volatility / inconsistency. Daily revenues swing widely; some days great, some terrible. Increases business risk: cash flow becomes unpredictable, inventory and staffing are harder to plan. May be acceptable in high‑reward industries (startups, seasonal businesses) but dangerous for stable operations.

• Low _____ → High consistency / low risk. Revenues are stable and predictable. Excellent for planning, budgeting, and meeting loan obligations. However, if mean is low, consistent poor performance is still a problem.

Standard Deviation (SD)

• High ______ → Same as high SD but in squared units (e.g., dollars squared). In business, high variance means very unstable performance across time periods or locations. For a chain of stores, high variance in sales suggests some branches are doing very well while others are failing.

• Low ______ → All observations are close to each other. All stores perform similarly, or daily sales are nearly identical. Good for standardization and forecasting.

Sample Variance

• High ______ (Leptokurtic, >3 or excess >0) → More extreme outliers than a normal distribution. In revenue, this means occasional very high or very low sales days happen more often than expected. High risk: a few catastrophic days or windfall days. Business must keep cash reserves for bad days and capacity for huge spikes.

• Low ______ (Platykurtic, <3 or excess <0) → Fewer extreme outliers. Most days are near the average. This is low‑risk, stable revenue. Good for predictable industries (utilities, subscriptions), but may miss out on occasional big gains.

Kurtosis (Tailedness

• High Positive ______ (right tail) → Most revenue days are low, but few days are extremely high (e.g., Black Friday sales). Mean > Median. Business implication: you depend on rare big events. Cash flow is usually low, so you need to manage survival through lean periods.

• High Negative _____ (left tail) → Most days are high, but few days are extremely low (e.g., a restaurant closed due to snowstorm). Mean < Median. Business is usually strong, but occasional disasters. Focus on preventing those rare failures.

• Skewness near zero → Symmetric distribution. Mean and median are close. Normal, predictable business environment.

Skewness

High ______ → Very large difference between the best and worst performance. Suggests unstable business cycles, seasonal spikes, or inconsistent quality. Could be fine for seasonal businesses (e.g., ice cream shops) but problematic for steady operations.

Low _______ → All values fall within a narrow band. Very consistent performance. Good for forecasting but might indicate lack of growth or rigidity.

Range

• High _____ → Even the worst day/month is still high. This is a very healthy business: no bad days. Indicates strong floor, low risk of failure.

• Low ______ → The worst performance is very poor (e.g., zero sales, huge loss). Even if average is good, the business has vulnerability. Consider safety nets: emergency fund, diversifying income.

Minimum

• High _____ → The best performance is outstanding. Could be a one‑time event (big contract, holiday rush) or a sign of growth potential. Use to set capacity limits and celebrate success.

• Low ______ → Even the best day is low. Indicates the business has a low ceiling – limited market, poor pricing, or operational bottlenecks. May need a new strategy to break out.

Maximum

• High ____ → Over the observed period, the business generated a large total revenue, profit, or volume. Directly good for top‑line growth. But check other stats: a high sum could come from many low‑value transactions or few high‑value ones.

• Low _____ → Total performance is poor. Could mean low volume, low prices, or short time period. Compare across similar periods (e.g., monthly sums) to detect trends.

Sum

• High ______ → Many observations (e.g., many customers, many days, many transactions). Gives statistical reliability – means, SD, etc. are more trustworthy. In business, high customer count usually good if each transaction is profitable.

• Low _____ → Few observations. High uncertainty – a single bad day can distort the mean. May indicate low traffic, small sample size, or niche market. Decisions based on low count are risky.

Count