Chapter 6 and Midterm 1 Review

Cheat Sheet for Excel Commands and Statistical Concepts

Exam Preparation Strategies

• Students are urged to create a cheat sheet for exam preparation.

• The cheat sheet should include:

  • Key Excel commands

  • Relevant examples

  • Important topics from the course

• Use the cheat sheet in conjunction with Cengage and practice exams on student portals.

Importance of Familiarity with the Cheat Sheet

• Familiarize yourself with the location of information on the cheat sheet.

• Know which chapters and specific sections relate to questions on the exam.

• Regular usage of the cheat sheet increases comfort with the material.

Test Logistics

• The exam will take place on the class portal.

• No laptops or cell phones are allowed; only designated PCs should be used.

Normal Distribution

• Definition: Normal distribution refers to the shape of data that is symmetrical around the mean.

• Parameters:

  • $\mu$ (mu): Represents the mean of the distribution.

  • $\sigma$ (sigma): Represents the standard deviation of the distribution.

• The shape of a normal distribution looks like a bell curve and can be characterized as symmetrical.

Notations and Terminology

• Random Variable: The data observed in a statistical study (e.g. GPAs, exam scores, sales figures).

  • Denoted as $x$.

• The exam scores are assumed to be normally distributed with specific values given as examples (e.g. Mean = 75, Standard Deviation = 5).

Z-scores

• Definition: A z-score indicates how many standard deviations an element is from the mean.

• Calculation: For a given value $x$:
  $\text{Z} = \frac{x - \mu}{\sigma}$.

• Example:

  • For an exam score of 75:

  • $\text{Z} = \frac{75 - 75}{5} = 0$ (indicating it is average).

  • For an exam score of 70:

  • $\text{Z} = \frac{70 - 75}{5} = -1$ (indicating it is 1 standard deviation below the mean).

Area Under the Curve and Percentages

• The area under the normal distribution curve represents the relative frequency or percentages of data.

• To find the percentage of scores below a certain value, the Excel command used is: $\text{NORM.DIST}(x, \mu, \sigma, \text{TRUE})$.

  • Example for score < 70:

  • $\text{NORM.DIST}(70, 75, 5, TRUE)$

• For scores greater than a certain value, use:
  $1 - \text{NORM.DIST}(x, \mu, \sigma, \text{TRUE})$.

Excel Commands for Common Scenarios

• Percentage of Grades Less than a Number:

  • Command:
    $\text{NORM.DIST}(x, \mu, \sigma, \text{TRUE})$.

  • Example for x = 70:

  • $\text{NORM.DIST}(70, 75, 5, TRUE)$

• Percentage of Grades Greater than a Number:

  • Command:
    $1 - \text{NORM.DIST}(x, \mu, \sigma, \text{TRUE})$.

  • Example for x = 90:

  • $1 - \text{NORM.DIST}(90, 75, 5, TRUE)$.

Finding Areas between Two Values

• To find the percentage of data between two values $a$ and $b$:

  • Command:
    $\text{NORM.DIST}(b, \mu, \sigma, \text{TRUE}) - \text{NORM.DIST}(a, \mu, \sigma, \text{TRUE})$.

  • Example for scores between 80 and 90:

  • $\text{NORM.DIST}(90, 75, 5, TRUE) - \text{NORM.DIST}(80, 75, 5, TRUE)$.

Finding Cutoff Points

• To find the cutoff point for grades corresponding to a certain percentile, the command is: $\text{NORM.INV}(p, \mu, \sigma)$.

  • Where $p$ is the percentile.

Understanding Standard Scores (Z-scores)

• For a specific percentile:

  • The Excel command for Z-scores is:
    $\text{NORM.S.INV}(p)$.

• Example for top 10% cut-off:

  • $\text{NORM.S.INV}(0.90)$.

Measures of Central Tendency in Data Analysis

• Mean: Average of a data set.

• Median: Middle value when data is ordered.

• Mode: Most frequently occurring value in a data set.

• Use median for skewed data sets for a better measure of central tendency.

Variability and Coefficient of Variation

• Definition of Variability: Indicates how much the data varies.

• Coefficient of Variation:

  • Formula:
    $CV = \frac{\sigma}{\mu} \times 100$.

  • Useful for comparing variability between datasets with different units or means.

Sampling Techniques

• Samples should ideally be random to avoid Selection Bias.

• Descriptive Statistics: Describe a data set (mean, median, etc.) of a population.

• Inferential Statistics: Draw general conclusions from a sample to infer about the larger population

Conclusion

• Familiarize yourself with commands, units, and examples.

• Practice using Excel to solidify understanding of statistical concepts and calculations.

• Review all chapters thoroughly before the exam and utilize the cheat sheet effectively.