lesson 2

• Grouped Frequency Distribution

  Grouping data into classes to simplify large datasets and facilitate easier analysis
• Grouped Frequency Distribution

  • Helps in organizing raw data into meaningful categories or intervals
  • Makes it easier to identify patterns, trends, and outliers
  • Reduces the complexity of data presentation, making it more understandable to stakeholders
  • Summarizes and interprets data effectively, allowing for clearer communication of findings
• Class number

  Sequential numbering or labeling of the different groups or intervals into which the data is divided
• Class interval

  Range of values covered by each group or category in a frequency distribution
• Class width

  Difference between the upper and lower limits of a class interval
• Calculating class width

  1. R= Xmax-Xmin

  2. K= 1+3.3 log (n)

  3. CW= R/K
• Central tendency

  Statistical measure to determine a single score that defines the center of a distribution
• Goal of central tendency

  To find the single score that is most typical or most representative of the entire group
• Arithmetic mean

  Sum of the scores divided by the number of scores
• Median

  Midpoint of the list when scores are ordered from smallest to largest
• Mode

  Score or category that has the greatest frequency
• Formulas for central tendency measures

  1. Population Mean = μ

  2. Sample Mean = X̄

  3. Arithmetic Mean for Ungrouped Data Set = ∑X/N

  4. Arithmetic Mean for Grouped Data Set = ∑fX/N

  5. Weighted Mean for Two Data Sets = ∑X1 + X2/N1 + N2
• Central Tendency Exercises 2.1-2.8

  • Computation and analysis of mean, median, and mode for various data sets
• Variability

  Quantitative measure of the differences between scores in a distribution, describing the degree to which the scores are spread out or clustered together
• Variability

  • Provides information about the distribution of scores
  • Tells whether the scores are clustered close together or spread out over a large distance
  • Measures how well an individual score (or group of scores) represents the entire distribution
• Variability

  A quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together
• If the scores in a distribution are all the same, then there is no variability
• Variability

  • It describes the distribution of scores, specifically whether the scores are clustered close together or spread out over a large distance
  • It measures how well an individual score (or group of scores) represents the entire distribution
• Range

  The distance covered by the scores in a distribution, from the smallest to the largest score
• Interquartile Range

  The range between the boundaries cutting off the middle 50% of scores from the 25% below and the 25% above
• Calculating Interquartile Range

  1. Split the distribution into quarters (quartiles)

  2. Take the range of the middle two quarters (middle 50%)

  3. Ignore the extreme quarters
• Average/Mean Deviation (AD)

  The average deviations of all the scores away from the mean, calculated without regard to whether the score is above or below the mean
• Variance (σ²)

  The average of the squared deviations from the mean
• Standard Deviation (σ)

  The square root of the variance, providing a measure of the standard, or average, distance from the mean
• Relationship between σ² and σ

  Taking the square root of the variance (σ²) cancels out the squared units, resulting in a measure (σ) that is in the same units as the original data
• – 2.75
• N = 20
• ∑f X = 1855
• ∑ = 69.75
• EXERCISE 3.5: 𝝈𝟐 and 𝝈 for Ungrouped Data Set

  1. ∑ 𝑓 𝑋 − 𝑋 2

  𝑁

  2. 𝜎 = 1.868
• EXERCISE 3.6: 𝝈𝟐 and 𝝈 for Ungrouped Data Set

  1. ∑ 𝑓 𝑋 − 𝑋 2

  𝑁

  2. 𝜎2 = 1.881

  3. 𝜎 = 1.371
• EXERCISE 3.7: 𝝈𝟐 and 𝝈 for Ungrouped Data Set

  1. ∑ 𝑓 𝑋 − 𝑋 2

  𝑁

  2. 𝜎2 = 1.798

  3. 𝜎 = 1.341
• EXERCISE 3.8: 𝝈𝟐 and 𝝈 for Grouped Data Set

  1. ∑ 𝑓 𝑚 − 𝑋 2

  𝑁

  2. 𝜎2 = 2628.36

  3. 𝜎 = 51.268
• EXERCISE 3.9: 𝝈𝟐 and 𝝈 for Grouped Data Set

  1. ∑ 𝑓 𝑚 − 𝑋 2

  𝑁

  2. 𝜎2 = 7.4016

  3. 𝜎 = 2.721
• EXERCISE 3.10: 𝝈𝟐 and 𝝈 for Grouped Data Set

  ∑ 𝑓 𝑚 − 𝑋 2

  𝑁
• Sampling error is the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter
• Margin of error

  Tells you how many percentage points your results will differ from the real population value
• There always will be some "margin of error" when sample statistics are used to represent population parameters
• Ways to Calculate MoE

  1. Find the critical value of the confidence interval

  2. Find the Standard Error of Mean (SEM) using the standard deviation

  3. Multiply the critical value from Step 1 by the standard deviation or standard error from Step 2
• Confidence Level

  • 99%
  • 95%
  • 90%
  • 80%