Data Analysis and Interpretation
Summarising numbers
Descriptive statistics condense a column into a few values. Measures of centre: mean (arithmetic average, uses every value), median (middle value when sorted, robust to extremes), mode (most frequent, the only sensible option for nominal data). Measures of spread: range (max − min, sensitive to outliers), interquartile range (Q3 − Q1, the middle 50%), variance (average squared deviation) and standard deviation (square root of variance, in the original units).
Choose median and IQR for skewed data such as income, house prices or call durations; choose mean and standard deviation for roughly symmetric data. A quick skew check: if the mean sits noticeably above the median, the distribution is right-skewed.
Frequency and relationships
Pivot tables and COUNTIF-style aggregation produce frequency distributions; a histogram shows the shape of one numeric variable. Correlation (r between −1 and +1) measures the strength and direction of a linear relationship. An r near 0 means no linear relationship - there may still be a strong curved one. Correlation never establishes causation; a confounding variable can drive both.
Inference and bias
Sample results estimate the population with uncertainty. Larger samples reduce random sampling error but not bias. Watch selection bias (who is in the data), survivorship bias (only successes remain), response bias and convenience sampling. Stratified sampling ensures key groups are represented; random sampling gives each unit an equal chance.
Traps
Averaging ordinal ratings as if they were interval; quoting percentage-point changes as percentages (20% to 25% is +5 points but +25%); comparing counts without a common denominator; ignoring base rates; reading a forecast as certainty.
Worked example
Salaries (thousands): 20, 22, 25, 27, 30, 150. Mean = 45.7, median = 26. One extreme value drags the mean upward, so report the median - and investigate the 150 as an outlier or a different population.