In a research study examining the distribution of household income in a small town, the data appears to be negatively skewed. Which of the following statements accurately describes negative skew?
B: The majority of households have income below the mean.
Negative skew, or left skew, means that the tail of the distribution is on the left side, and most data points are concentrated on the right side, below the mean.
Answer choice A: Negative skew is a measure of data spread, is incorrect. Negative skew is not a measure of data spread. It describes the shape of the distribution, specifically the elongated tail on the left side of the data.
Answer choice C: The majority of households have income above the mean, is incorrect. Negative skew does not imply that that majority of households have income above the mean; it’s the opposite.
Answer choice D: The majority of households have income close to the mean, is incorrect. In an negatively skewed distribution, the majority of data points are below the mean, not close to the mean.
Answer choice E: The mean, median, and mode are all equal, is incorrect. In a negatively skewed distribution, the mean is leass than the median which is less than the mode.
Key Learning Point
Negative skew, also known as left skew, occurs when the tail of the distribution is on the left side, and indicating that mean < median < mode. The tail is due to outliers on the left side of the curve.
