Statistics, Probability and Matrices: notes

Averages

• Mean: total / number of items. 2, 4, 9 has mean 15 / 3 = 5.
• Median: the middle value when ordered. For an even count, average the middle two.
• Mode: the most common value. Range: largest minus smallest.
• Grouped data: estimate the mean using the middle of each class: sum of (frequency x midpoint) / total frequency.
• Cumulative frequency: a running total. Read the median at half the total and the quartiles at a quarter and three quarters.

Charts

• Pie chart: angle = (frequency / total) x 360.
• Histogram: the area of a bar shows frequency when class widths differ.

Probability

• Probability = favourable outcomes / total outcomes, between 0 and 1.
• Not happening: P(not A) = 1 - P(A).
• Mutually exclusive events: P(A or B) = P(A) + P(B).
• Independent events: P(A and B) = P(A) x P(B).
• Tree diagram: multiply along the branches, add between the branches.

Matrices

• Add and subtract matrices of the same order, entry by entry.
• Multiply: rows of the first by columns of the second. A 2 by 2 times a 2 by 1 gives a 2 by 1. Order matters: AB is not usually BA.
• Determinant of (a b / c d) = ad - bc. The inverse is 1/det x (d -b / -c a). No inverse if det = 0.