Statistics: J shaped & Reverse J Shaped Distribution in Urdu Hindi Saima Academy скачать в хорошем качестве

Statistics: J shaped & Reverse J Shaped Distribution in Urdu Hindi Saima Academy

In statistics, J-shaped and reverse J-shaped distributions describe specific patterns in data that resemble the letter "J" or its mirror image when plotted. These shapes are useful in identifying patterns in frequency distributions or histograms. 🔹 J-Shaped Distribution 📈 Description: A J-shaped distribution starts with a high frequency of lower values, then decreases slightly or remains low, followed by a sharp increase in frequency at the higher end of the range. The shape resembles a “J”: low on the left, rising steeply to the right. ✅ Characteristics: Positive skew (right-skewed) Few small values and a lot of large values Long tail on the right 📊 Example: Income distribution in some populations (many people earn less, and a few earn a lot) Age of diagnosis for certain late-onset diseases 🔍 Example Data Pattern: Value: 1 2 3 4 5 6 7 8 9 Freq: 2 1 1 2 3 5 8 12 18 🔹 Reverse J-Shaped Distribution 📉 Description: A reverse J-shaped distribution begins with a high frequency at lower values and then quickly decreases as values increase. Looks like a backward "J": high on the left, dropping off quickly to the right. ✅ Characteristics: Negative skew (left-skewed) Many small values, few large ones Long tail on the left 📊 Example: Survival times after a fatal disease diagnosis Age at death in infant mortality (many die early, fewer later) 🔍 Example Data Pattern: Value: 1 2 3 4 5 6 7 8 9 Freq: 20 12 8 5 3 2 1 1 1 🔁 Comparison Summary: Feature J-Shaped Reverse J-Shaped Skewness Right (positive) Left (negative) Tail direction Long right tail Long left tail Frequency trend Starts low → high Starts high → low Example High-income earners Infant mortality