Which among the following is the statistical measure that indicates the peakedness of distribution ?

Question

Accepted Answer

The correct option is 4:
Kurtosis is the correct statistical measure that specifically indicates the peakedness or flatness of a frequency distribution relative to a normal distribution. In more technical terms, it is the fourth moment about the mean. It tells us how concentrated the data is around the mean and provides information about the tails of the distribution. A high kurtosis (leptokurtic) means the distribution is more peaked with fatter, heavier tails, implying a greater chance of extreme values. Conversely, a low kurtosis (platykurtic) indicates a flatter peak and thinner tails than a normal distribution.

The incorrect option is 1:
Skewness is the statistical measure that quantifies the degree of asymmetry in a distribution. It determines whether the data values are relatively spread out or concentrated more toward the left (negative skew) or the right (positive skew) of the mean. While it describes a shape characteristic, its focus is on the lack of symmetry, not the vertical dimension or peakedness of the central part of the curve.

The incorrect option is 2:
Correlation is a measure used to describe the linear relationship between two distinct variables. It indicates the strength and direction (positive or negative) of the relationship between them. Correlation is a bivariate statistic, meaning it requires two sets of data, and it is entirely unrelated to the peakedness, or any other characteristic of the shape, of a single variable's distribution.

The incorrect option is 3:
The Mean is the most common measure of central tendency, calculated as the arithmetic average of all data points. Its purpose is solely to locate the center of the distribution. It is one of the key descriptive statistics but offers absolutely no information about the shape characteristics of the distribution, such as its peakedness, symmetry, or spread.