Question

QUESTION 11 How can you use the mean, the median, and the mode to determine whether data are skewed? Interpret the following relationships between mean, median, and mode in terms of skow (matching) a) mode < median < mean A. No skew b) mode > median mean > B. positive skew c) mode = median = mean C. negative skew

Answer 1

One can use the mean, median, and mode to determine skewness in a dataset. If mode < median < mean, it indicates a positive skew. If mode > median > mean, it indicates a negative skew. When these measures are equal, it suggests no skew but does not always mean perfect symmetry.

Step-by-step explanation:

In mathematics, the mean, median, and mode are three measures of central tendency that can help determine whether a data set is skewed.

In a perfectly symmetrical data set, the mean, median, and mode are equal. When mode < median < mean, the data are said to be positively skewed. A positive skew implies that the majority of data points fall to the left of the mean, with a long tail of a few high-value outliers to the right.

In scenarios where mode > median > mean, the data are characterized as having a negative skew. This means the majority of the data points are concentrated to the right of the average, with a long tail of low-value outliers to the left.

Option a) mode = median = mean would ideally indicate No skew, but it's important to note, this doesn't always suggest perfect symmetry in the data distribution.

Learn more about Data skewness