Final answer:
When the mean of a dataset is significantly lower than the median, as is the case with a mean of 23 and a median of 42, the data distribution is skewed right due to higher values pulling the tail of the distribution.
Step-by-step explanation:
When the mean and median of a set of data differ significantly, it often indicates that the data are not symmetrical. In the case where the mean is 23 and the median is 42, the data distribution is likely to be skewed. Because the median is higher than the mean, the data are skewed right or positively skewed. This means that there are a number of data points that are much higher than the mean which are pulling the right tail of the distribution outwards.
In comparison with a symmetrical distribution where the mean and median would be close or the same, the significant difference between these two measures of central tendency in the provided dataset suggests that the higher values are affecting the mean. Thus, the skewness is towards the higher numbers, making the distribution right-skewed.
Understanding that the mean is affected more by extreme values than the median, and when it is less than the median, the data tends to have a rightward skew and vice versa for a leftward skew. With this in mind, one can analyze the shape of the data distribution based on these central tendencies.