Math Problem Statement

Tabel menunjukkan nilai yang diperoleh oleh 50 orang peserta ujian statistik. Hitunglah nilai rata-rata, median, modus, buat grafik histogram, poligon, dan ogive, serta hitung variansi, koefisien variasi, kemiringan data (skewness), boxplot, dan berikan analisis serta interpretasi perhitungan.

Solution

Here are the calculated results for each part:

  1. Mean (Rata-rata): 49.1
  2. Median: 48.71 (approximated based on interpolation)
  3. Mode (Modus): 47.75
  4. Variance (Variansi): 215.04
  5. Coefficient of Variation (KV): 29.87%
  6. Skewness (Kemiringan Data): 0.08 (indicating a slight positive skew)

Graphs

  • Histogram: Shows the frequency distribution across score intervals.
  • Frequency Polygon: Plots frequency values with a connecting line across intervals.
  • Ogive (Cumulative Frequency): Displays cumulative frequency, useful for determining median and quartiles.
  • Boxplot: Visualizes the distribution with quartiles and highlights any potential outliers.

Analysis and Interpretation:

  • The mean and median are quite close, suggesting the distribution is nearly symmetric.
  • A slight positive skewness implies a minor tail on the higher side of the score distribution.
  • Variance and KV indicate the spread of data, showing some variability but with a moderate concentration around the central values.

Would you like further details on any specific part or have additional questions?

Additional Questions to Consider:

  1. How would the interpretation change if there was a significant skewness in the data?
  2. What impact does the coefficient of variation have on understanding data spread?
  3. How could outliers affect the mean and variance of this dataset?
  4. Why is the mode located near the middle of the distribution?
  5. How can we use the cumulative frequency (ogive) to find percentiles?

Tip: When analyzing skewness, consider whether the tail indicates an unusual concentration of higher or lower values, as it impacts data interpretations in real-world contexts.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Data Analysis

Formulas

Mean (Rata-rata) = Σ(f * x) / Σf
Median = L + [(n/2 - F) / f] * i
Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * i
Variance (σ^2) = Σ(f * (x - μ)^2) / N
Coefficient of Variation (CV) = (σ / μ) * 100%
Skewness = (3 * (Mean - Median)) / Standard Deviation

Theorems

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Suitable Grade Level

College Level