Topic 6 - Statistics and Probability (Year 1 HL class)
(A) List of Topics and Content to be Taught
So in this section, we will simply introduce basic concepts. We will divide our investigation into three sections (i) descriptive statistics, (ii) basic probability and (iii) modelling data
| Objective | Topic | Content | Teaching Emphasis |
| 6.1 | Basic concepts of Descriptive Stats | population | |
| sample | |||
| random sample | |||
| discrete and continuous data | |||
| frequency distributions of data | |||
| 6.2 | Presentation of Data and Associated concepts | frequency tables and diagrams | |
| box and whisker plots | |||
| mid-interval values | |||
| interval width | |||
| upper and lower interval boundaries | |||
| frequency histograms | |||
| 6.3 | Measures of Central Tendency | mean, median, mode | demonstrate how to find on a GDC |
| quartiles and percentiles | |||
| range & interquartile range | |||
| variances - sample and population | |||
| standard deviation | |||
| 6.4 | Cumulative Data | Cumulative frequency graphs | demonstrate how to find on a GDC but also on hand-drawn graphs |
| finding medians, quartiles, percentiles on cumulative frequency graphs | |||
| 6.5 | Basic concepts of Probability | concepts of trial, outcome, sample space (U), and events | |
| probability of an event P(A) = n(A)/n(U) | |||
| complementary events A and A` (not A) | |||
| P(A) + P(A`) = 1 | |||
| 6.6 | Combined Events | P(AUB) = P(A) + P(B) - P(AB) | |
| P(AB) = 0 for mutually exclusive events | |||
| 6.7* | Conditional Probability | the formula P(A|B) = P(AB)/P(B) | |
| the formula P(A|B) = P(A) = P(A|B`) for independent events | |||
| the formula P(AB) = P(A)xP(B) for independent events | |||
| use of Bayes' Theorem | |||
| 6.8 | Graphic Representations | use of Venn diagrams | incorporate throughout 6.5 - 6.7 |
| use of tree diagrams | |||
| use of tables | |||
| 6.9* | Discrete data | concept of discrete random variables and their probability distributions | |
| Expected value (mean), E(X) for discrete data, variance, standard deviation | |||
| 6.10* | Binomial Distribution | Binomial Distribution and the mean and variance of the distribution | |
| Poisson distribution, its mean and variance | |||
| 6.11 | Normal Distribution | Properties of the Normal Distribution | use the GDC and tables |
| Standardization of normal variables |
(B) Timing/Pacing
We require 40 hours and at 1.33333 hrs/class, we require 30 classes, but we have set our schedule for 28 lessons (which is 9 weeks) plus one period for a unit exam.
But for Topic 6, we will use 28 class periods (36 hours of class time) and maybe some weekend review classes (2) to cover the material, which will get us finished by the second week in November
(C) Sequence of Topics
The relevant sections in the textbook are as follows:
Chapter 18 - Descriptive Statistics (2 weeks)
(18A) - Continuous Numerical Data
(18B) - Measuring the Center of Data
(18C) - Cumulative Data
(18D) - Measuring the Spread of Data
(18E) - Stats using Technology
(18F) - Variance and Standard Deviation
(18G) - The Significance of Standard Deviation
Chapter 19 - Probability (3 weeks)
(19A) - Experimental Probability
(19B) - Sample space
(19C) - Theoretical Probability
(19D) - Using Grids to Find Probabilities
(19E) - Compound Events
(19F) - Using Tree diagrams
(19G) - Sampling with and without replacement
(19H) - Binomial Probabilities
(19I) - Sets and Venn Diagrams
(19J) - Laws of Probability
(19K) - Independent events revisited
(19L) - Probabilities Using Permutations and Combinations
(19M) - Bayes' Theorem
Chapter 30 - Statistical Distributions (3-4 weeks)
(30A) - Discrete Random Variables
(30B) - Discrete Probability distributions
(30C) - Expectation
(30D) - The Mean and Standard Deviation of a Discrete Random Variable
(30E) - Expected Values
(30F) - The binomial distribution
(30G) - Mean and Standard Deviation of a Binomial Random Variable
(30H) - The Poisson Distribution
(30I) - Continuous Probability Density Functions
(30J) - Normal Distributions
(30K) - The Standard Normal Distribution
(30L) - Applications of the Normal Distribution
(D) Schedule and Calender
| Monday | Tuesday | Wednesday | Thursday | Friday |
| Aug 29
Day 1 |
Aug 30
Day 2 L1 6.1 - Basic concepts of Descriptive Stats & 6.2 - Presentation of Data (Text 18A,E) |
Aug 31
Day 3 |
Sep 1
Day 4 L2 6.1 - Basic Concepts of Descriptive Stats & 6.2 - Presentation of Data (Text 18A,E) |
Sep 2
Day 5 L3 6.3 - Measures of Central Tendency - Mean, Median, Mode (Text 18B,E) |
| Sep 5
Day 1 |
Sep 6
Day 2 L4 (Text 18C,E) |
Sep 7
Day 3 |
Sep 8
Day 4 L5 6.3 - Measuring the Spread of Data - Range,Quartiles, Percentiles (Text 18D,E) |
Sep 9
Day 5 L6 6.3 - Measures of Central Tendency - Variance and Standard Deviation (Text 18F,G) |
| Sep 12
Day 1 |
Sep 13
Day 2 L7 6.3 - Measures of Central Tendency - Variance and Standard Deviation (Text 18F,G) |
Sep 14
Day 3 TOK RETREAT for Year 1 Students |
Sep 15
Day 4 L8 TOK RETREAT for Year 1 Students |
Sep 16
Day 5 L9 TOK RETREAT for Year 1 Students |
| Sep 19
Day 1 |
Sep 20
Day 2 L10 QUIZ Chapter 18 6.5 - Basic Concepts of Probability (Text 19A-D) |
Sep 21
Day 3
|
Sep 22
Day 4 L11 6.6 - Combined Events - Dependent, Independent Events (Text 19E,F,G) |
Sep 23
Day 5 L12 |
| Sep 26
Day 1 |
Sep 27
Day 2 L13 6.6 - Combined Events - Sets & Venn Diagrams (Text 19I) |
Sep 28
Day 3 |
Sep 29
Day 4 L14 6.7 - Conditional Probability &Independent Events (Text 19J,K) |
Sep 30
Term 1 Holiday |
| Oct 3
Day 5 L15 (Text 19M) |
Oct 4
Day 1 |
Oct 5
Day 2 L16 6.6 - Binomial Probabilities - The Fundamental Counting Principle & 6.6 - Binomial Probabilities - Permutations (Handout from other texts)
|
Oct 6
Day 3 |
Oct 7
Day 4 L17 6.6 - Binomial Probabilities - Combinations (Handouts from other texts) |
| Oct 10
Day 5 L18 View Lesson as PowerPoint Presentation (Handouts from other texts) |
Oct 11
Day 1 |
Oct 12
Day 2 L19 6.9 - Discrete Random Variables & Distributions View Lesson as PowerPoint Presentation (Text 30A,B) |
Oct 13
Day 3 |
Oct 14
Day 4 L20 QUIZ Chapter 19 6.9 - Discrete Random Variables - Mean and Standard Deviations View Lesson as PowerPoint Presentation (Text 30D) |
| Oct 17
Day 5 L21 6.9 - Discrete Random Variables - Mean and Standard Deviations View Lesson as PowerPoint Presentation (Text 30C,E) |
Oct 18
Day 1 |
Oct 19
Day 2 L22 View Lesson as PowerPoint Presentation (Text 30F) |
Oct 20
Day 3 |
Oct 21
Day 4 L23 6.10 - Binomial Distributions, Means, and Standard Deviations View Lesson as PowerPoint Presentation (Text 30G) |
| Oct 24
Day 5 L24 6.10 - The Poisson Distribution View Lesson as PowerPoint Presentation (Text 30H) |
Oct 25
Day 1 |
Oct 26
Day 2 L25 6.11 - Continuous Probability Density Functions & Normal Distributions (Text 30I,J)
|
Oct 27
Day 3 |
Oct 28
Day 4 L26 6.11 - Standard Normal Distribution View Lesson as PowerPoint Presentation (Text 30K) |
| Oct 31
HOLIDAY |
Nov 1
HOLIDAY |
Nov 2
HOLIDAY
|
Nov 3
HOLIDAY |
Nov 4
HOLIDAY |
| Nov 7
Day 5 L27 6.11 - Standard Normal Distribution - Applications View Lesson as PowerPoint Presentation (Text 30L) |
Nov 8
Day 1 L28 |
Nov 9
Day 2
6.11 - Standard Normal Distribution - Applications View Lesson as PowerPoint Presentation (Text 30L) |
Nov 10
Day 3 L29 |
Nov 11
Day 4 |