05.02 Literasi Data

Main ideas / concepts conveyed

• Data literacy topic: Explains how to analyze the shape of a distribution using descriptive statistics, with emphasis on whether the data is sorted or not sorted.
• Four distribution measures mentioned:
  • Central tendency: median and mean (without sorting)
  • Spread / distribution: discussed in relation to central tendency and earlier spread context
  • Skewness (asymmetry): how far distribution tails extend to the left/right
  • Sharpness / kurtosis (peakedness & tail heaviness)
• Sorted vs. not-sorted approaches:
  • Some measures use formulas that require ordering (e.g., percentiles/quantiles).
  • The presenter contrasts:
    • Sorted statistics (e.g., quartiles/percentiles)
    • Unsorted data summaries (e.g., mean and observational aggregates)

Methodology / instructional content (organized in steps)

1) Compute distribution measures (conceptual framework)

• Measure central tendency

  • Use median when ordering (sorting) is relevant.
  • Use mean when not relying on sorted statistics.

• Assess skewness (tail direction and asymmetry)

  • Skewness indicates whether data are:
    • Right-skewed (positive skew): more mass on the left/lower values; tail extends to the right.
    • Left-skewed (negative skew): more mass on the right/higher values; tail extends to the left.

• Assess kurtosis / sharpness

  • Mesokurtic: similar to a normal distribution (often described as kurtosis ≈ 3); tails are neither too heavy nor too light.
  • Leptokurtic: kurtosis > 3; more concentration in the middle with heavier tails and potential outliers.
  • Platykurtic (implied): kurtosis < 3; distribution is more evenly spread (uniform-like shape), typically fewer/no outliers.

2) Determine skewness and kurtosis using different approaches

The lecture highlights that skewness/kurtosis calculations can differ depending on whether the data is sorted.

A. When data are sorted

• Use Bowley and Kelly approaches:
  • Both rely on quantiles/percentiles computed from ordered data.
  • The approaches differ in how they select/weight portions of the distribution:
    • Bowley: uses half of the data (quartile-type logic).
    • Kelly: uses percentiles, specifically described using the 10th and 90th percentiles to capture a broader central/tail structure (about 80% coverage between them).
• Key implication: both require computing ordered statistics (quartiles/percentiles).

B. When data are not sorted

• Use unsorted-statistics-based formulas:
  • Uses average/aggregate observation values rather than quartile/percentile positions.
  • Skewness and kurtosis may differ from Bowley/Kelly because unsorted formulas rely on different information (e.g., whole-sample moments vs. order-based measures).

3) Distribution peak / modes (shape characterization)

• Discuss whether the distribution is:
  • Single-peaked or multiple-peaked, described by the number of modes (how many peaks appear).

4) Fit distribution visually (histogram + overlay curve)

• Create a histogram.
• Overlay a theoretical curve to visually evaluate how well the candidate distribution matches the data.

5) Case study workflow: claims from 100 companies

• Dataset: Monthly number of claims from 100 companies

  • Example range mentioned: from Company 1 = 233 claims to Company 100 = 284 claims.

• If not sorting:

  • Compute average, variance, and standard deviation (referenced as explained earlier).

• If using sorted statistics:

  • Compute quartiles (described as a centralization measure).
  • With 100 observations, compute percentiles more finely:
    • from the 1st percentile through the 99th percentile.

• Percentile/order formula described:

  • The lecture states an order-of-I-th percentile idea such as:
    • order of I-th percentile ≈ (I/100)(N + 1)
  • For the later need for 10th and 90th percentiles, it notes the difference around the 10th/11th ordered observations and the role of interpolation.

• Compute skewness and kurtosis using both approaches:

  • Bowley vs. Kelly produces different skewness values (expected due to different quartile/percentile spans).
  • Kurtosis also differs by approach:
    • one method yields positive kurtosis
    • another yields negative kurtosis
  • Interpretation: skewness/peakedness/sharpness characteristics can vary depending on the method used.

6) Complement with graphical summaries

• Dot-box (box-dot) plot

  • Advantage: highlights outliers.
  • Example case conclusion:
    • Data appears symmetrical (left/right tails are similar).
    • No obvious outliers detected.
  • Skewness direction:
    • Bowley and Kelly skewness are positive, suggesting concentration in smaller values.

• Stem-and-leaf plot

  • Advantage: shows raw data values and their frequency distribution by group.
  • Noted relationship:
    • Rotating it counterclockwise resembles a histogram, but it preserves raw values unlike a standard histogram.

7) Hypothesis testing based on distribution/correlation (example with regression/correlation)

• Hypothesis testing goal: verify whether an observed relationship is statistically supported.

• Example variables:

  • Y, X1, X2 (and correlations between pairs)

• Correlation interpretation:

  • Correlation near 1 indicates a strong linear relationship.
  • Smaller correlation implies weaker linear relationship.

• Test statistic procedure (as presented):

  • Compute a test statistic t (formula referenced but not fully shown).
  • Compare it to a critical point.
  • Example numbers given:
    • Test statistic = 24.9
    • Critical point = 2.1

• Decision & conclusion:

  • Reject H0 because the test statistic exceeds the critical point.
  • Conclude there is evidence of a linear relationship between Y and X1 (described with “P strength” and “wire length” in the example).

Main lessons / takeaways

• Distribution shape can be described using central tendency, skewness, and kurtosis.
• Skewness/kurtosis can change depending on whether you use:
  • sorted order statistics (Bowley/Kelly via quartiles/percentiles), or
  • unsorted moment-based formulas (using overall summary values).
• Visual tools like histograms with fitted curves, box-dot plots, and stem-and-leaf plots help confirm properties such as symmetry and outliers.
• Hypothesis testing can support claims about relationships (e.g., linear correlation/regression), not only descriptive summaries.

Speakers / sources featured

• Kurnia Novitasari — lecturer, Statistics Science Group (FMIPA ITB) (speaker throughout the lecture).
• “Brothers and sisters / thank you for your attention” — audience address by the lecturer (no other named sources).