The aim of the standard level content in the statistics and probability topic is to introduce students to important concepts, techniques and representations used in statistics and probability and their meaningful application in the real world. Students should be given the opportunity to approach this topic in a practical way, to understand why certain techniques are used and to interpret the results. The use of technology such as simulations, spreadsheets, statistics software and statistics apps can greatly enhance this topic.

It is expected that most of the calculations required will be carried out using technology, but explanations of calculations by hand may enhance understanding. The emphasis is on choosing the most appropriate technique, and understanding and interpreting the results obtained in context.

In examinations, students should be familiar with how to use the statistics functionality of allowed technology.

At SL the data set will be considered to be the population unless otherwise stated

– *Mathematics: applications and interpretation guide*

#### Mean from Data in Class

- Video - Distribution using Class Tables (3:12)
- Video - Understanding Mean from Grouped Data (3:30)
- Video - Mean from Grouped Data by Frequency Table (2:51)
- Video - Missing Frequency Values from Frequency Class Table (4:07)
- Topic - Discrete Intervals of 4
- Topic - Discrete Intervals of 9
- Topic - Discrete Intervals of 19
- Topic - Continuous Intervals
- Topic - Finding Frequencies

#### Median

- Video - Calculating the Median (3:01)
- Video - Median of Odd Scores (1:17)
- Video - Median of Even Scores (1:50)
- Video - Finding Missing Scores Given Median (2:32)
- Video - New Median by Additional Scores (2:11)
- Video - Introduction to a Median (5:22)
- Video - Median of Odd Scores from a Frequency Table (3:38)
- Video - Median of Repeated Even Scores from a Frequency Table (2:22)
- Video - Median of Non-Repeated Even Scores from a Frequency Table (2:26)
- Topic - Median: Odd Number of Scores
- Topic - Median: Even Number of Scores
- Topic - Median in Distribution
- Topic - Median in Frequency Table of Odd Scores
- Topic - Median in Frequency Table of Even Scores

#### Mean

- Video - Calculating Mean (0:46)
- Video - Calculating Mean with Frequencies (0:47)
- Video - Calculating Mean using Calculators (3:59)
- Video - Calculating Mean with Frequencies using Calculators (7:39)
- Video - Calculating the Mean (2:31)
- Video - Calculating the Mean of Different Units (1:41)
- Video - Calculating New Mean by Adding Additional Scores (2:34)
- Video - Finding Unknown Scores from Mean (2:01)
- Video - Understanding Mean from UnGrouped Data (2:35)
- Video - Mean from UnGrouped Data by Frequency Table (1:03)
- Video - Missing Frequency Values from Frequency Table (3:02)
- Video - Finding Mean (2:51)
- Topic - Effects to Mean of Adding Constant to Each Score in Data Set
- Topic - Effects to Mean of Subtracting Constant to Each Score in Data Set
- Topic - Effects to Mean of Multiplying Constant to Each Score in Data Set
- Topic - Effects to Mean of Dividing Constant to Each Score in Data Set
- Topic - Effects to Mean of Mixed Operations to Each Score in Data Set

#### Range and Interquartile Range

- Video - Understanding Range (1:30)
- Video - Finding Interquartile Range from Even Number of Data (6:19)
- Video - Finding Interquartile Range from Odd Number of Data (2:21)
- Video - Understanding Interquartile Range (3:07)
- Video - Finding Interquartile Range from Even Number of Scores (6:24)
- Video - Finding Interquartile Range from Odd Number of Scores (4:18)

#### Standard Deviation

- Video - Calculating Standard Deviation using Tables (2:42)
- Video - Calculating Standard Deviation with Frequencies using Tables (2:32)
- Video - Calculating Standard Deviation using Calculators (5:13)
- Video - Calculating Standard Deviation with Frequencies using Calculators (7:25)
- Video - Standard Deviation and Data Consistency (1:26)

#### Variance and Standard Deviation

- Video - Finding the Variance (7:20)
- Video - Find the Variance using Expectation Theorems (5:11)
- Video - Finding unknown value given the Variance (6:13)
- Video - Standard Deviation and Dispersion (4:29)
- Video - Calculating Standard Deviation by Calculators (3:37)
- Video - Calculating Standard Deviation with Frequency by Calculators (3:56)
- Video - Standard Deviation and Consistency (1:39)
- Video - Evaluation by Standard Deviation (3:42)

#### Cumulative Frequency Graphs and Ogive

- Video - Reading Cumulative Frequency Histogram (5:33)
- Video - Drawing Cumulative Frequency Histogram (1:46)
- Video - Reading Cumulative Frequency Polygon (3:26)
- Video - Interquartile Range from Cumulative Frequency Polygon (1:14)
- Video - Measure of Dispersion using Cumulative Frequency Graph (6:28)
- Video - Median from a Cumulative Frequency Graph (7:32)
- Video - Sketching Cumulative Frequency Graphs for Finding Median (2:30)
- Video - Reading Cumulative Frequency Graphs (4:43)
- Video - Median from a Grouped Cumulative Frequency Graph (5:56)

#### Box-and-Whisker Plots

- Video - Constructing Box-and-Whisker Plots (3:19)
- Video - Stem-and-Left Plots to Box-and-Whisker-Plots (3:19)
- Video - Drawing Box-and-Whisker Plots from Even Number of Scores (9:49)
- Video - Reading Box-and-Whisker Plots (6:40)
- Video - Drawing Box-and-Whisker Plots from Stem-and-Leaf Plots (8:37)
- Video - Drawing Box-and-Whisker Plots from Odd Number of Scores 1 (8:07)
- Video - Drawing Box-and-Whisker Plots from Odd Number of Scores 2 (2:09)

#### Introduction to Probability

- Video - Basic Probability (11:40)
- Video - Standard Pack of 52 Cards (11:18)
- Topic - Basic Properties of Probability
- Topic - Informal Description of Chance: Drag
- Topic - Informal Description of Chance: Multiple Choice
- Topic - Informal Description of Chance: True or False
- Topic - Informal Description of Chance: Likely

#### Experimental Probability

- Video - Estimating Probabilities from Data (5:13)
- Video - Understanding Regular Pack of 52 Cards (2:52)
- Video - Solving Regular Pack of 52 Cards Problems involving Probability (4:57)
- Video - Probability of Choosing All Different Suits from Regular Pack of 52 Cards (3:31)
- Video - Probability involving Dice (7:22)
- Video - Probability involving Sum of Faces of Dice (2:20)
- Video - Probability involving Product of Faces of Dice (6:01)
- Topic - Counting Number of Cards
- Topic - Probability using Regular Pack of 52 Cards
- Topic - Two Digit Numbers by Dice
- Topic - Sum of Two Dice

#### Laws of Probability

- Video - Addition of Probabilities (9:59)
- Video - Addition Rule of Probability (3:59)
- Video - Addition Rule of Probability involving Mutually Exclusive Events (5:53)
- Video - Product Rule of Probability (5:28)
- Video - Product Rule of Probability Involving Repeated Occurrences (5:34)
- Video - Probabilities involving Addition Rule and Product Rule (2:18)
- Video - Probability involving Number Digits 1 (5:40)
- Video - Probability involving Number Digits 2 (1:28)
- Topic - Addition Law of Probability
- Topic - Probability Regarding OR
- Topic - Addition Rule of Probability and Mutually Exclusive Events
- Topic - Probability Regarding AND
- Topic - Product Rule and Independent Events

#### Complementary Events

- Video - Understanding Complementary Events (15:28)
- Video - Probability of Events using At Least 1 (4:31)
- Video - Probability of Events using At Least 2 (8:49)
- Video - Probability of Events using At Most (2:00)
- Video - Arithmetic Calculation of Probability (1:22)
- Topic - Probability with At Least
- Topic - Probability with Ratios
- Topic - Probability of Complement Events without Replacement

#### Sets and Venn Diagrams

- Video - Understanding Venn Diagrams (2:43)
- Video - Drawing Venn Diagrams and Sets (2:20)
- Video - Drawing Venn Diagrams and Subsets (0:55)
- Video - Drawing Venn Diagrams and Mutually Exclusive Sets (0:48)
- Video - Representing Data in Venn Diagrams (3:40)
- Video - Probabilities in Venn Diagrams (5:01)
- Topic - Sets and Venn Diagrams

#### Tree Diagrams

- Video - Basic Tree Diagrams (5:03)
- Video - Tree Diagrams involving Percentages (7:45)
- Video - Tree Diagrams involving Independent Events (3:44)
- Video - Tree Diagrams involving Compound Events (7:15)
- Video - Tree Diagrams involving Twice as Likely (6:31)
- Video - Asymmetrical Tree Diagrams (2:10)
- Video - Probability involving Probability Tree 1 (2:34)
- Video - Probability involving Probability Tree 2 (2:35)
- Video - Probability involving Probability Tree 3 (2:39)
- Topic - Play with Tree Diagrams

#### Conditional Probability

- Video - Theory of Conditional Probability (5:46)
- Video - Techniques of Conditional Probability (1:30)
- Video - Conditional Probability in Multiple Events (16:32)
- Video - Conditional Probability in Continuous Random Variables (4:35)
- Video - Conditional Probability in Venn Diagrams (4:46)
- Topic - Conditional Probability Formula 1
- Topic - Conditional Probability Formula 2

#### Dependent Events

- Video - Dependent Events involving Orders (1:47)
- Video - Dependent Events in Choosing Books (5:42)
- Video - Dependent Events involving Birthdays (2:00)
- Video - Probability involving Dependent Events 1 (2:38)
- Video - Probability involving Dependent Events 2 (3:12)
- Video - Probability involving Dependent Events 3 (3:27)

#### Independent Events

- Video - Definition of Independent Events (7:09)
- Video - Basic Independent Events (4:46)
- Video - Independent Events in Tables (2:05)
- Video - Independent Events in Ordering Events (4:44)
- Video - Independent and Compound Events (4:07)
- Video - A Pair of Regular Dice (3:46)
- Video - Independent Events (1:00)
- Video - Probability involving Independent Events 1 (1:37)
- Video - Probability involving Independent Events 2 (3:10)
- Video - Probability involving Independent Events 3 (3:54)
- Video - Probability involving Independent Events 4 (1:33)
- Topic - Determining Independent & Dependent Events
- Topic - Pairing Independent Events

#### Sampling With Replacement

- Video - Probability with Replacement (6:07)
- Video - Probability with Replacement Excluding Duplicates (3:33)
- Video - Probability of Events with Replacements 1 (2:36)
- Video - Probability of Events with Replacements 2 (2:14)
- Video - Probability of Events with Replacements 3 (1:48)
- Topic - Sampling with Replacement

#### Sampling Without Replacement

- Video - Probability Without Replacement (5:57)
- Video - Probability without Replacement involving Ordering Events (4:30)
- Video - Probability Without Replacement involving Counting Techniques (4:55)
- Video - Probability without Replacement involving Specific Orders (6:42)
- Video - Probability without Replacement involving Selection of Items (6:04)
- Video - Probability without Replacement involving Raffles (4:01)
- Video - Probability of Events without Replacements (4:07)
- Video - Representing Events Without Replacements in Venn Diagrams (4:48)
- Video - Tree Diagrams involving Without Replacement (5:49)
- Topic - Sampling without Replacement
- Topic - Probability without Replacement with Complement Events
- Topic - Probability without Replacement with AND OR
- Topic - Probability without Replacement and Order of Events

#### Expected Value

- Video - Positive Financial Expectation (5:26)
- Video - Negative Financial Expectation (2:29)
- Topic - Financial Expectations involving Tossing a Coin
- Topic - Financial Expectations involving Tossing Three Coins
- Topic - Financial Expectations involving Throwing a Fair Die
- Topic - Financial Expectations involving Throwing Two Fair Dice
- Topic - Financial Expectations involving Percentages
- Topic - Financial Expectations involving Lottery