For a negatively skewed distribution with a mode of X = 25 and a median of 20, the mean is probably ____.
a. greater than 25
b. less than 20
c. between 20 and 25
d. cannot be determined from the information given
To determine the mean of a negatively skewed distribution, we need to consider the relationship between the mean, median, and mode.
In a negatively skewed distribution, the tail of the distribution is stretched toward the lower values. This means that there are more values on the higher end of the distribution.
Given that the mode of the distribution is 25, it suggests that 25 is the most frequently occurring value in the dataset.
Given that the median is 20, it indicates that 50% of the values in the dataset are below 20 and 50% are above 20.
Since the mean is affected by extreme values, the fact that the distribution is negatively skewed suggests that there are some extreme values on the lower end which drag the mean down.
Therefore, in this scenario, the mean is most likely less than 20 (Choice b - less than 20) because the negative skewness pulls the mean towards the lower values.
Answer: b. less than 20