T7 Mathematics Exam: Mean, Median, Mode, Range, and Probability 📊

Mean, Median, Mode

Definitions

• Mean: The average of a data set.
• Median: The middle number in a data set.
• Mode: The most frequent number in a data set.

Steps

• Arrange numbers in numerical order before calculation.

Mean Calculation Example

1. Sum of all numbers: 127.
2. Number of values: 10.
3. Mean: 127 / 10 = 12.7 (or 13 when rounded up).

Median Calculation Example

1. Arrange numbers in order.
2. If the number of values is odd, the median is the middle number.
3. If even, the median is the average of the two middle numbers.
   • In this case: Median of [2, 14] ➡️ (2 + 14) / 2 = 13.

Mode Calculation Example

1. Arrange numbers in order.
2. Mode (most frequent number): 10 (appears 3 times).

Practice Examples

• Pain Scores:
  • Mean: 4.4
  • Median: 4
  • Modes: 3, 4
• Cookie Sales:
  • Mean: 13
  • Median: 12
  • Mode: 12

Range Calculation

Definition

• The range is the difference between the highest and lowest numbers in a data set.

Example Calculation

• Data Set: [2, 10]
  • Range: 10 - 2 = 8
• Data Set: [73, 96]
  • Range: 96 - 73 = 23

Practice Example

• Quiz Scores: [76, 82, 85, 88, 91]
  • Range: 91 - 76 = 15

Distribution Shapes

Symmetrical Distributions

• Symmetric Distribution: Mean = Median. Data is mirrored on both sides.
• Bimodal: Two peaks, indicating two most frequent values.
• Unimodal: One peak, Mean = Median = Mode.
• Uniform: Equal frequency across all values, no peaks.
• Roughly Uniform: Close to uniform but not exact.

Skewed Distributions

• Left-Skewed: Mean < Median (Bulk of data is on the right).
• Right-Skewed: Mean > Median (Bulk of data is on the left).
• Use toe directions analogy to better understand.

Practice Questions

• Two Peaks in Data Set: Bimodal
• Even Frequency: Uniform
• Most Data on Lower End: Right-Skewed

Probability

Definition

• Probability Equation: Total number of favorable outcomes / Total number of possible outcomes.

Basic Examples

• Coin Toss: Heads or Tails, 50% each (1/2).
• Dice Roll: 6 faces, each with 1/6 probability.

Probability Line

• Range: 0 (impossible) to 1 (certain).
• 1/2 represents a 50% chance.

Complex Examples

• Dice Roll: 1/6 ➡️ 0.167 ➡️ 16.7%
• Spinner with 16 sections: 1/16 ➡️ 6.25%
  • For multiple outcomes: Total number of successful outcomes / Total number of possible outcomes.

Practice Question

• Marble Example:
  • Total Marbles: 10
  • Drawing Two Reds:
    • First draw: 5/10
    • Second draw (without replacement): 4/9
    • Combined Probability: (5/10) * (4/9) = 2/9

Important Tips

• Use and to indicate multiplying outcomes.
• Use or for adding outcomes.

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I hope this guide helps in understanding the core concepts of mean, median, mode, range, distribution shapes, and probability. Be sure to practice and organize data properly to save time during exams. Good luck!