Math Problem Statement
Solution
Here are the calculated results for each part:
- Mean (Rata-rata): 49.1
- Median: 48.71 (approximated based on interpolation)
- Mode (Modus): 47.75
- Variance (Variansi): 215.04
- Coefficient of Variation (KV): 29.87%
- 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:
- How would the interpretation change if there was a significant skewness in the data?
- What impact does the coefficient of variation have on understanding data spread?
- How could outliers affect the mean and variance of this dataset?
- Why is the mode located near the middle of the distribution?
- 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
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