Final answer:
In a negatively skewed distribution, the mode is typically the greatest value, followed by the median, and then the mean, which is pulled toward the tail and is usually the smallest.
Step-by-step explanation:
In a negatively skewed distribution, which of the following will be the greatest value? The answer is (b) mode. In a negatively skewed, or left-skewed, distribution, the tail of the distribution is stretched out to the left, and the bulk of the data values, including the mode, are located on the right.
The relationship among the mean, median, and mode in a skewed distribution shows that the mean is pulled toward the tail, and reflects the skewing the most, the median is less affected by extreme values, and the mode is least affected by skewness. Therefore, in a negatively skewed distribution, the mode is typically the greatest value, followed by the median, and then the mean, which is usually the smallest. This is due to the longer tail of low values pulling the mean down more than the median.
To provide a clearer understanding, consider a set of data that is negatively skewed: 1, 2, 2, 3, 3, 3, 4. The mode (most frequent value) is 3, the median (middle value) is 3, and the mean (average) would be less than 3 because the low values (particularly the 1) pull the average down.