Descriptive Statistics

Descriptive statistics summarise a distribution's centre, spread and shape, so we can understand data without reading every row.

s = df["alcohol"]

print("Mean     :", s.mean())
print("Median   :", s.median())
print("Mode     :", s.mode().iloc[0])
print("Std      :", s.std())
q1, q3 = s.quantile([0.25, 0.75])
print("IQR      :", q3 - q1)
print("Skewness :", s.skew())
print("Kurtosis :", s.kurt())     # excess kurtosis (normal = 0)

1. Mean

The average: sum of all values divided by the number of observations.

Best for: roughly symmetric data without extreme values, e.g. comparing average income across departments.
Not suitable: skewed data or data with outliers - extreme values pull the mean away from the typical value.
Example: average monthly sales of a store over a year.

Numeric illustration: salaries 30, 32, 33, 35, 400 (thousand). Mean = 106 - nobody earns near 106.

2. Median

The middle value after sorting. Half the values are below it, half above. It is robust to outliers.

Best for: skewed data or data with outliers.
Not suitable: when you need every value's magnitude to count (it ignores how far the other values are).
Example: household incomes - a few very rich households distort the mean, so the median is the better "typical" value.

For the salaries above the median is 33 - a much fairer summary.

3. Mode

The most frequent value or category.

Best for: categorical or discrete data, e.g. the best-selling product in a campaign.
Not suitable: continuous measurements such as height or weight, where exact repeats are rare.
Example: which product was sold the most.

A dataset may have no mode, one mode, or several (bimodal, multimodal).

4. Standard deviation (std)

The typical distance of values from the mean. Low std = values close to the mean; high std = widely spread.

Best for: measuring variability, e.g. day-to-day variation in website traffic.
Not suitable: heavily skewed data or data with outliers, since it is sensitive to them.
Example: an e-commerce site with big spikes on sale days has a high std of daily visits.

For roughly normal data: about 68% of values lie within 1 std of the mean, 95% within 2 std, 99.7% within 3 std.

5. Interquartile range (IQR)

IQR = Q3 - Q1, the spread of the middle 50% of the data. Robust to outliers.

Best for: describing spread when outliers are present and detecting outliers (the 1.5 x IQR rule).
Not suitable: when you need the spread of the whole data including extremes (use range or std then).
Example: the range of scores of the middle half of a class, ignoring a few unusually high or low scores.

Outlier fences: lower = Q1 - 1.5 x IQR, upper = Q3 + 1.5 x IQR.

6. Skewness

Measures asymmetry: does the distribution lean right (positive) or left (negative)?

Best for: deciding whether a transformation is needed before algorithms sensitive to skew (linear regression).
Not suitable: for data already symmetric - skewness is near zero and adds little.
Example: monthly sales of a product with holiday peaks are right-skewed; apply a log transform to stabilise variance.

Skewness	Interpretation
-0.5 to +0.5	approximately symmetric
0.5 to 1 (or -1 to -0.5)	moderately skewed
beyond +/-1	highly skewed

7. Kurtosis

Measures tailedness: heavy tails (many extreme values) versus light tails, compared with a normal distribution.

Best for: finding datasets with more outliers than expected. High kurtosis warns about extreme values that can hurt some models.
Not suitable: near-normal data where tails are not of interest.
Example: daily stock returns. High kurtosis signals possible extreme loss days, so use robust statistics or adjust risk models.

pandas reports excess kurtosis (normal = 0). Positive = heavier tails than normal; negative = lighter tails.

Comparison of mean and median: a quick diagnostic

Relationship	Likely shape
mean = median	symmetric
mean greater than median	right-skewed
mean less than median	left-skewed

Group summaries

df.groupby("quality")["alcohol"].agg(["count", "mean", "median", "std", "min", "max"])