Statistics (university) · Part 01
Describing data
Summarise a pile of numbers with averages, spread and shape.
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- Types of dataData is either categorical (labels, like eye colour) or numerical (amounts, like height). Numerical data is discrete if you count it (goals scored) and continuous if you measure it (time in seconds).
- MeanThe mean is the sum of all values divided by how many there are. It is the usual meaning of average.
- Median and modeThe median is the middle value when data is sorted. The mode is the value that appears most often. Both ignore how extreme the largest and smallest values are.
- SkewnessSkewness describes lopsided data. Right-skewed data has a long tail of large values. Left-skewed data has a long tail of small values. The mean gets pulled toward the tail.
- Standard deviationThe standard deviation measures how far values typically sit from the mean. A small value means the data is bunched up. A large value means it is spread out. It uses the same units as the data.
- Sample varianceSample variance divides the sum of squared gaps by n minus 1, not n. This corrects for the fact that a sample sits closer to its own mean than to the true population mean.
- Quartiles and IQRQuartiles cut sorted data into four equal groups. Q1 is the median of the lower half, and Q3 is the median of the upper half. The interquartile range (IQR) is Q3 minus Q1, the width of the middle half.
- OutliersAn outlier is a value far from the rest. A common rule marks a value as an outlier if it lies more than 1.5 times the IQR below Q1 or above Q3.
- z-scoreA z-score says how many standard deviations a value is from the mean: (value minus mean) divided by standard deviation. Positive means above the mean, negative means below.