Which statement is true about the data shown in a histogram?

When analyzing a histogram, the relationship between the mean and median can often be inferred based on the shape of the distribution. In this case, if the correct answer identifies that the mean is probably smaller than the median, it suggests that the histogram is skewed to the left.

In left-skewed distributions, also known as negatively skewed distributions, the tail on the left side of the histogram is longer or fatter than the right side. This can pull the mean toward the lower values, while the median, being the middle value, remains less affected by the extreme low values. As a result, the mean ends up being less than the median. This typical behavior of the mean and median reflects their sensitivity to different aspects of data distribution.

Understanding these relationships helps in interpreting the data accurately. It’s important to visualize the histogram to check for skewness, which provides insight into whether the mean or median is affected more significantly by the shape of the data distribution. In scenarios where the distribution is symmetric, the mean and median will be equal. Therefore, recognizing the skewness can guide one to make informed statements about the relationship between these two measures of central tendency.