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Stats Summary 😾📊

What you just learned, compressed into tables and graphs, 'cause your brain can only handle so much

Listen up, data padawan

You just went through a bunch of stats shit. Medians, percentiles, quartiles, skewness, kurtosis... it's enough to make a normal person cry. But you're not normal. You're here. So let me summarize everything in two clean tables because apparently you people love organized suffering. These tables show you what matters and what you should remember before you embarrass yourself in the real world.

So below, to jot down your amoeba 🧬 brain of yours, are the graphs of our last Aggregated Table: the histogram and the cumulative graph.

WHY?🤔 So you can relate to the statistics summary tables of the data bruh!🤦‍♂️

Absolute Frequency Distribution

Histogram with Frequency Polygon Overlay

0 10 20 30 40 35 25 10 20 10 Absolute Frequency Distribution Class Interval Absolute Frequency (Fᵢ)
Histogram Bars (Absolute Frequency)
Frequency Polygon
The red line connects the midpoints of each class interval, showing the distribution shape.

Cumulative Absolute Frequency (Ogive)

Less-than Cumulative Frequency Polygon

0 25 50 75 100 35 60 70 90 100 Cumulative Absolute Frequency Distribution Class Interval Cumulative Absolute Frequency (Fᵢ)
Histogram Bars (Cumulative Frequency)
Ogive (Cumulative Frequency Line)
The red line shows the cumulative frequency, useful for finding percentiles and quartiles.
📈
The "What Even Is This Distribution?" Table
Statistic Symbol Value What It Tells You
Sample Size N 100.0000 You have 100 observations. Not great, not terrible.
Mean μ 14.3250 Average value. The "center" if you ignore outliers.
Median Me 13.0000 Middle value. 50% below, 50% above. Robust to outliers.
Mode M0 10.8621 Most frequent value. Apparently 10.86 is popular here.
Variance σ² 59.5569 How spread out your data is. Squared units, because math.
Standard Deviation σ 7.7173 Average distance from mean. In original units. Useful.
Coefficient of Variation CV 0.5387 Relative variability. σ/μ. 53.87% variation relative to mean.
Skewness (Pearson) G1 0.4487 Positive skew. Right tail longer. Mean > Median.
Skewness (Bowley) G2 0.2190 Also positive. Quartile-based. Confirms the right-skew.
Kurtosis K 0.3267 Compared to ref 0.263: Platykurtic. Flatter than normal.
💡 Key Takeaway: Your distribution is right-skewed (mean > median > mode) and flatter than a normal distribution. There's more spread in the tails than you'd expect. The data is moderately variable (CV ≈ 54%).
📊
The "Where Do I Stand?" Percentile Table
Percentile Value What It Means Formula Used
P5 (5th percentile) 3.1429 Only 5% of values are below this. The sad bottom. l + a × [(pN - cum_f_prev) / f]
P10 (10th percentile) 4.2857 Bottom 10% cutoff. You're in trouble if you're here. l + a × [(0.1N - cum_f_prev) / f]
Q1 (25th percentile) 7.7143 First quartile. 25% below, 75% above. Lower quarter. l + a × [(0.25N - cum_f_prev) / f]
Median / Q2 / P50 13.0000 The middle. Half above, half below. The "typical" value. l + a × [(0.5N - cum_f_prev) / f]
Q3 (75th percentile) 21.2500 Third quartile. Top 25%. You're above average if here. l + a × [(0.75N - cum_f_prev) / f]
P90 (90th percentile) 25.0000 Top 10% cutoff. You're killing it if you're here. l + a × [(0.9N - cum_f_prev) / f]
P95 (95th percentile) 28.5000 Top 5%. Elite territory. Probably outliers. l + a × [(0.95N - cum_f_prev) / f]
Interquartile Range (IQR) 13.5357 Q3 - Q1. Middle 50% spread. Robust range measure. Q3 - Q1
Mean Absolute Deviation (DAM) 6.7400 Average absolute distance from mean. Less sensitive to outliers than variance. Σ|xᵢ - μ| / N
🎯 Pro Tip: The IQR (13.54) is your "typical spread" ignoring extremes. Compare it to the range (P95 - P5 = 25.36) to see how much outliers stretch things. Here, middle 50% is about half the total spread - so yeah, outliers matter.

🧠 What Your Brain Should Retain (TL;DR Version)

Distribution Shape

Right-skewed (mean > median). Tail extends to higher values. Not symmetric, so normal distribution assumptions might fail.

Spread & Variability

Standard deviation (7.72) is about half the mean (14.33). That's moderate to high variability. Data points are pretty scattered around the mean.

Central Tendency

Mean (14.33), Median (13.00), Mode (10.86) all different → confirms skewness. Median is your "typical" value, mean gets pulled up by high values.

Percentile Reality Check

If you score 25+, you're in the top 10%. Below 4.29? Bottom 10%. Middle 50% are between 7.71 and 21.25 (IQR).

Outlier Alert

P95 (28.5) is way above Q3 (21.25). That gap suggests high outliers exist. They're pulling the mean up, making it larger than the median.

Kurtosis Check

Distribution is platykurtic (K > 0.263). Flatter peak than normal distribution. More probability in the shoulders, less in center/tails.

😾 Final Word from Evil Math Cat: You now have the numbers. You know the shape. You see the spread. Don't just report the mean like a basic bitch - talk about the skew, the percentiles, the IQR. Your data has personality (right-skewed, flattish). Respect it. Now go apply this without embarrassing me.