In a distribution, if the mean is less median, then the distribution is said to be –
The user provided the correct answer as . [Answer Text], but since the options are A-D with no labels, I need to infer the answer based on the question. The question is about skewness in distributions. When the mean is less than the median, the distribution is skewed to the left, or negatively skewed. So the correct answer is probably "negatively skewed" or "left skewed."
Let me recall the core concept. In statistics, the mean being less than the median indicates a left skew because the tail is on the left. The median is less affected by extreme values, so if the mean is pulled left by outliers, the median remains higher.
For the explanation, the core concept is about skewness in data distributions. The correct answer is that the distribution is negatively skewed. The wrong options might be positive skew, symmetric, or uniform. I need to explain why each is incorrect. For example, positive skew would have mean > median, symmetric has mean ≈ median, uniform is even spread.
Clinical pearl: Remember that skewness direction is determined by the tail. If mean < median, tail is left, so left skew. Mnemonic: "Left Tail, Less Mean." Putting it all together, the correct answer is the one that states the distribution is negatively skewed. The options might have been labeled as such. Let me structure the explanation with the required sections and make sure to follow the formatting rules. Also, check the character count to stay within limits. Need to be concise but thorough.
**Core Concept**
This question tests understanding of **skewness in statistical distributions**. In a **negatively skewed (left-skewed)** distribution, the mean is less than the median due to a long tail extending toward the left, pulling the mean downward. Conversely, **positively skewed (right-skewed)** distributions have a mean greater than the median.
**Why the Correct Answer is Right**
A **negatively skewed distribution** has a tail on the left side (lower values), which pulls the mean below the median. The median remains closer to the bulk of the data, while the mean is influenced by extreme low values. For example, in income data where most people earn moderate incomes but a few earn extremely low amounts, the mean income would be less than the median.
**Why Each Wrong Option is Incorrect**
**Option A:** *Positively skewed* is incorrect because a right-skewed distribution has a mean **greater** than the median.
**Option B:** *Symmetrical* is incorrect because symmetry implies mean = median.
**Option C:** *Uniform* is incorrect because a uniform distribution lacks skewness (mean = median = mode).
**Clinical Pearl / High-Yield Fact**
Remember the mnemonic: **"Left Tail, Less Mean"** (negative skew) and **"Right Tail, Greater Mean"** (positive skew). This is a high-yield concept for interpreting data in research and clinical trials.