If a frequency distribution is positively skewed, the mean of the distribution would be :

Question

Accepted Answer

The correct option is 1: A positively skewed distribution (or right-skewed distribution) is characterized by a long tail extending to the right side of the graph. In statistics, the shape of the distribution dictates the relative positions of the three main measures of central tendency: the Mean, Median, and Mode. Skewness arises when the data set contains extreme values (outliers) on one side. When a distribution is positively skewed, the extreme large values on the right pull the Mean in the direction of the long tail. The Mode, representing the most frequently occurring value, remains at the peak of the distribution (the left side). Consequently, the Median is positioned between the Mode and the Mean. Therefore, the relationship among these measures in a positively skewed distribution is always: Mean > Median > Mode. Thus, the mean is greater than the mode. The incorrect option is 2: Smaller than Mode describes a negatively skewed (or left-skewed) distribution. In this case, the long tail extends to the left, and the extreme small values pull the Mean below the Mode, resulting in the relationship Mean \< Median \< Mode. The incorrect option is 3: Equal to Mode applies to a perfectly symmetrical distribution, such as the normal distribution. In a symmetrical distribution, the Mean, Median, and Mode coincide at the exact center of the data set, meaning Mean = Median = Mode. The incorrect option is 4: Zero is a specific value and does not describe a relational position in skewness unless the mean of the dataset itself happens to be zero. The mean of a frequency distribution is rarely zero in real-world data unless the data is centered precisely around zero, which is unrelated to the concept of positive skewness itself.