If for a sample data - Mean < Median < Mode, then the distribution is

Correct Option (D)

The condition Mean < Median < Mode is a definitive characteristic of a negatively skewed distribution, also referred to as skewed to the left. In such a distribution:

• The tail of the distribution extends towards the lower values on the left side.
• The majority of the data points are concentrated towards the higher values on the right side.
• The mode represents the peak frequency, followed by the median, and the mean is pulled towards the longer left tail due to the influence of lower values.

Incorrect Options:

Option (A) symmetric: A symmetric distribution, such as a normal distribution, is characterized by the equality of its measures of central tendency: Mean = Median = Mode. This contradicts the given condition where Mean < Median < Mode.

Option (B) skewed to the right: A distribution skewed to the right (positively skewed) is characterized by the relationship Mean > Median > Mode. This is the inverse of the condition provided in the question.

Option (C) neither symmetric nor skewed: The specific ordering of Mean < Median < Mode unequivocally indicates a distinct form of skewness. Therefore, the distribution is not "neither symmetric nor skewed"; it exhibits a clear leftward skew.