Final answer:
The statement is true since, in a left-skewed distribution, the median is typically higher than the mean due to the tail of lower values pulling the mean down.
Step-by-step explanation:
The statement is true: In a left-skewed distribution, the median tends to be higher than the mean. Left-skewed distributions, also known as negatively skewed, occur when data have a tail extending to the left. In such cases, the bulk of the data values (including the median and mode) lie to the right of the mean. This phenomenon occurs because the mean is pulled towards the long tail of the distribution, which contains lower values, hence resulting in a mean that is less than the median.
For instance, if a distribution has a mean of 6.3, a median of 6.5, and a mode of 7, this indicates a left-skewed distribution where the mean is pulled toward the tail, reflecting more extreme lower values. The median minimally reflects the skewing, whereas the mode typically corresponds to the highest frequency of data and is less affected by extreme values.
Understanding the relationship between the mean, median, and mode is crucial when analyzing data distributions. It helps in interpreting statistical results correctly and making informed decisions based on the data.