1.In a skewed distribution with a long right tail like the distribution of annual
incomes in most developing countries, which of the following statements is
true?
mean<mode<median
mean<median<mode
mode<mean<median
mode<median<mean

In a skewed distribution with a long right tail, known as positively skewed, the mean is pulled toward the extreme high values by outliers, positioning it furthest right. The median, as the middle value, lies between the mode (peak frequency, leftmost) and the mean. Annual incomes in developing countries exemplify this, with most earning modestly while few have extreme wealth.​​

Option Analysis

• mean < mode < median: Incorrect for right skew; applies to left-skewed (negative) distributions where the tail pulls the mean leftward.​

• mean < median < mode: Also wrong; describes negative skew with mode rightmost.​

• mode < mean < median: Invalid; mean exceeds median in positive skew due to right tail influence.​

• mode < median < mean: Correct; mode peaks left, median centers data, mean shifts right from outliers like high incomes.​​

In skewed distribution with long right tail, such as annual incomes in developing countries, understanding the mean median mode order is crucial for statistics and CSIR NET Life Sciences preparation. A positively skewed distribution features most values clustered left with a stretched right tail from outliers, shifting central tendencies predictably.​

Positively Skewed Distribution Explained

Long right tail indicates positive skewness, where extreme high values (e.g., top earners) dominate less frequent outcomes. The mode occurs at the highest frequency peak, typically lowest. Median splits data 50/50, resisting outliers better than mean, which averages all values and gets dragged rightward. Thus, mode < median < mean always applies.​​

Real-world example: Income data shows billions at low-moderate levels, few ultra-wealthy—mean exceeds median (middle earner), both above mode (common wage).​

Why Annual Incomes Fit Perfectly

Annual incomes in developing countries exhibit high positive skew due to inequality: Gini coefficients rise in places like India, China. Extreme wealth pulls mean up, while mode and median reflect masses better for policy. Symmetric distributions equalize all three; negative skew reverses order.​

This skewed distribution long right tail pattern aids exam questions on central tendency.