UPSC NDA I 2022 Mathematics Solved Paper

Concept:Skewness measures the asymmetry of a unimodal frequency distribution.For a left-skewed (negatively skewed) curve, the tail is longer on the left side, and most data points cluster to the right.In such a distribution, the three measures of central tendency follow the order: $\text{Mode} > \text{Median} > \text{Mean}$.Explanation:Identify the shape: A left‑skewed curve has a longer left tail and the peak (mode) lies to the right.The mode is the highest point of the distribution.The median is the middle value, and it lies between the mode and the mean in left‑skewed data.The mean is pulled toward the left tail by the extreme low values, making it the smallest.Thus the inequality $\text{Mode} > \text{Median} > \text{Mean}$ holds.Check the options: A and B list mean as the largest, which is incorrect for left‑skewness.Option C lists median > mean > mode, which is the order for right‑skewed data.Only option D matches the correct order for a left‑skewed curve.Answer:Option D: $\text{Mode} > \text{Median} > \text{Mean}$