For a negatively skewed distribution, which is the correct relation?

Correct option is A

In a negatively skewed distribution (left-skewed), the tail is longer on the left side of the peak. This means that the majority of data points are concentrated on the right, but a few lower values pull the mean to the left.

The relationship between the three central tendency measures in a negatively skewed distribution follows this order:

Mean < Median < Mode

• Mode represents the most frequently occurring value and is least affected by extreme values (outliers).
• Median is the middle value when data is ordered, making it moderately affected by skewness.
• Mean is significantly affected by extreme values (outliers), causing it to be lower than both the median and mode in a negatively skewed distribution.

Thus, the correct answer is (a) Arithmetic Mean < Median < Mode.

Additional Information:

·         In a positively skewed distribution (right-skewed):

• Mean > Median > Mode
• The mean is pulled to the right by extreme high values.

·         In a symmetric (normal) distribution:

• Mean = Median = Mode

·         Measures of central tendency usage:

• Mean is used for normally distributed data.
• Median is preferred when there are outliers or skewed distributions.
• Mode is useful for categorical data or unimodal distributions.