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Term 1
Unit 1 Correlation and regression: correlation, scatter diagrams, Pearson’s and Spearman’s coefficients, regression and the least squares line; Unit 2 Advanced measurements in statistics: stem-and-leaf plots, quartiles and their graphs, the semi-interquartile range; Unit 3 Probability: random experiments and events, the axioms of probability, conditional probability and independent events
1
Correlation and scatter diagrams
Correlation: direct and inverse relations between two variables, scatter diagrams and the scale of the correlation coefficient r from −1 to 1
2
Pearson’s correlation coefficient
Pearson’s linear correlation coefficient: the formula, the table of x, y, x², y² and xy, and finding r from given sums
3
Spearman’s rank correlation
Spearman’s rank correlation coefficient: ranks, tied values, D² and the formula, and when to use it instead of Pearson’s
4
Regression and the least squares line
Regression: predicting y from x, simple linear regression y = a + bx and the least squares method
5
Using the regression line
Using the regression line: predicting y, the error of a prediction, extrapolation and regression from given sums
6
Stem-and-leaf plots
Stem-and-leaf plots: building single and double plots with a key and reading the median, the mode and the range from them
7
Quartiles of lists and stem-and-leaf plots
Quartiles of single data and of stem-and-leaf plots: Q1, Q2 and Q3 by their order, with the rule for going between two values
8
Quartiles from frequency tables
Quartiles from a frequency table: ascending cumulative frequency, the quartile class and the formula, and the graphical method
9
Box plots and the semi-interquartile range
Box plots and the semi-interquartile range: the five numbers, drawing and reading boxes, and (Q3 − Q1) ÷ 2 from data, stem-and-leaf plots and frequency tables
10
Random experiments and sample spaces
Random experiments and sample spaces: coin and dice tables, tree diagrams, drawing with and without replacement, and events
11
Operations on events and equally likely outcomes
Operations on events, mutually exclusive events and the probability of an event when the outcomes are equally likely
12
The axioms of probability and their corollaries
Axioms of probability and their corollaries: 0 ≤ P ≤ 1, P(S) = 1, additivity, P(A′), P(A − B) and P(A ∪ B), and solving problems
13
Conditional probability
Conditional probability: the reduced sample space, P(A | B) = P(A ∩ B) ÷ P(B), the multiplication rule, two-way tables, tree and Venn diagrams
14
Independent and dependent events
Independent and dependent events: the test P(A ∩ B) = P(A) × P(B), drawing with and without replacement, and independent against mutually exclusive
15
Review of Term 1
Term 1 review: correlation and regression, quartiles and spread, probability, conditional probability and independence
☰ Year plan · Statistics
Egypt
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Secondary 3
›
Statistics
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Week 3
Spearman’s rank correlation
Week 3 · Spearman’s rank correlation coefficient: ranks, tied values, D² and the formula, and when to use it instead of Pearson’s · 3 lessons
Lesson 1
Lesson 2
Lesson 3
Quiz
8
Homework
5
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Week 3 ·
Spearman against Pearson on the same numbers, and ranking up or down: does ΣD² change?
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Week 3 · Homework
