Math 4thQ reviewer

Lesson 1: Measures of Variability

• Variability - How spread out or scattered the data is.

• Range - Difference between Highest and Lowest

• Mean - Average

• Median - Middle Value

• Mode - Most Repeated

Range = Highest - Lowest

Mean Deviation - Average of absolute differences between each value and the mean of the data.

Steps for Solving

1. Find the mean

2. Subtract the mean from each value

3. Take the absolute average

4. Find the average

Formula: 𝑀𝐷=∑|𝑥𝑖−𝑥̄|𝑛

Standard Deviation - How spread out the values in a data set are from the mean.

Steps for Solving

1. Find the mean

2. Subtract the mean from each value

3. Square each difference

4. Find the average

5. Take the square root

Formula: 𝜎=∑(𝑥𝑖−𝜇)2𝑁 for population data or 𝑠=∑(𝑥𝑖−𝑥̄)2𝑛−1 for sample data

Types of Graphs

• Bar graph - comparison/frequency

• Line graph - changes over time/trends

• Pie graph - percentages and proportions

Lesson 2: Probability

• Measure of expectation for an event to occur

P (E) = n (E)/n (S)

Types

• Theoretical - predicts the likelihood of an event based on mathematical reasoning and ideal conditions rather than actual experimentation.

TP = number of favorable outcomes/total number of possible outcomes

• Experimental - the likelihood of an event occurring based on actual data collected from experiments or trials.

EP = number of times an event occurs/total number of trials

Lesson 3: Fundamental Principles of Counting

• Multiplication Rule - The total number of possible outcomes for a series of events is calculated by multiplying the number of choices for each individual event.

Example: If you have 3 shirts, 2 pairs of pants, and 4 pairs of shoes, you can create 3×2×4=24 different outfits

• Addition Rule - It is used when you choose one option from multiple disjoint sets.

Example: A restaurant offers 5 different salads and 3 different soups. If you choose only one item (salad or soup), there are 5+3=8 total choices.