If mean, median and mode are 10, 18, 26 respectively, the distribution is :
First, I need to recall the relationship between mean, median, and mode in different types of distributions. In a normal distribution, these three measures are all equal. But when there's skewness, they differ. Skewness refers to the asymmetry in a distribution.
Positive skew (right skew) occurs when the tail on the right side is longer or fatter. In such cases, the mean is greater than the median, which is greater than the mode. So, mean > median > mode. On the other hand, negative skew (left skew) has a longer left tail, and the order is mode > median > mean.
Looking at the given numbers: mean is 10, median is 18, mode is 26. Here, the mode is the highest, followed by median, then mean. That would be mode > median > mean. That fits the pattern of a negative skew. So the distribution is negatively skewed.
Now, let me check the options again. The options aren't provided, but typically in such questions, the possible answers are right skew, left skew, normal distribution, or symmetric. Since the correct answer here is left skew (negative skew), the options must include that. The other options like right skew or normal distribution would be incorrect because the values don't fit those patterns.
To confirm, in a right skew, the mean would be the highest, followed by median, then mode. Here, that's not the case. Normal distribution would have all three measures equal. So the only possibility left is left skew, which matches the given values.
**Core Concept**
This question tests understanding of **skewness in statistical distributions**, specifically how the relationship between **mean, median, and mode** indicates the direction of skew. In a **negatively skewed (left-skewed)** distribution, the mode is highest, followed by the median, then the mean (mode > median > mean).
**Why the Correct Answer is Right**
The given data shows **mode (26) > median (18) > mean (10)**. This pattern is characteristic of a **left-skewed distribution**, where the tail extends toward the left (lower values). The mean is pulled toward the tail, making it the smallest value, while the mode remains at the peak of the distribution. This is a classic "negative skew" scenario.
**Why Each Wrong Option is Incorrect**
**Option A:** A **symmetrical distribution** (e.g., normal) would have mean = median = mode.
**Option B:** A **right-skewed (positive skew)** distribution has mean > median > mode.
**Option C:** **Bimodal distribution** is irrelevant here, as it involves two modes, not a skewness pattern.
**Clinical Pearl / High-Yield Fact**
Remember the mnemonic: **"Mean < Median Median > Mode → Right skew"**. This relationship is critical for interpreting skewed data in epidemiological or lab results.
**Correct Answer: D. Negatively skewed distribution**