Chapter 9. Statistics

Descriptive statistics summarize data [6][12].

Mean: the sum of values divided by their number.

Median: the middle value of ordered data.

Mode: the most frequent value.

Range: maximum minus minimum.

Standard deviation: s = √(Σ(x − x̄)² / (n − 1)) for a sample; σ = √(Σ(x − μ)² / N) for a whole population.

Displaying data. Histograms, box plots, scatter plots and bar charts. Choose a display that matches the type of variable (categorical or numerical).

Normal distribution. A symmetric, bell-shaped curve defined by mean μ and standard deviation σ. About 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations of the mean. A z-score, z = (x − μ)/σ, measures how many standard deviations a value lies from the mean.

Inference. A confidence interval gives a plausible range for a population parameter; a hypothesis test uses sample data to judge a claim about the population. A small p-value indicates data unlikely under the null hypothesis, but it does not measure the size or importance of an effect.

Correlation and causation. The correlation coefficient r ranges from −1 to 1 and measures linear association. A strong correlation does not by itself show that one variable causes the other.

Review: Find the mean and population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9. (Answer: mean 5, standard deviation 2.)