Question

Select the distribution in which value of the mean is maximum, mode is least and the median lies between mean and mode

• A. Symmetrical distribution
• B. Positively skewed distribution
• C. Negatively skewed distribution
• D. Bimodal distribution

Hint:

In a positively skewed distribution, the long right tail pulls the mean to the right of the median, making the mean the largest of the three measures of central tendency.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Skewness refers to the asymmetry of a probability distribution around its central mean.
In a skewed distribution, the relative positions of the three primary measures of central tendency—mean, median, and mode—deviate from their symmetrical alignment.

Step 2: Detailed Explanation:
Let us compare the relationships of the mean, median, and mode across different distribution types:
Symmetrical Distribution: The distribution is perfectly balanced. The mean, median, and mode are equal and located at the center of the distribution:
\[ \text{Mean} = \text{Median} = \text{Mode} \]
Positively Skewed Distribution: The distribution has a long tail extending toward the higher, positive values.
Because the tail pulls the mean toward the higher values, the mean is greater than the median.
The mode remains at the peak of the distribution, representing the most frequent value.
The median lies in the middle, representing the 50th percentile.
The mathematical relationship in a positively skewed distribution is:
\[ \text{Mean} > \text{Median} > \text{Mode} \]
In this distribution, the mean is the maximum value, the mode is the least, and the median lies between them.
Negatively Skewed Distribution: The distribution has a long tail extending toward the lower, negative values.
The relationship is:
\[ \text{Mode} > \text{Median} > \text{Mean} \]
Here, the mode is the maximum value and the mean is the least.

Step 3: Final Answer:
The described relationship represents a positively skewed distribution.