In statistical analysis, a box plot is a graph that can be a valuable source of easy-to-interpret information about a sample of study. A box plot can provide information about a sample’s range, median, normality of the distribution, and skew of the distribution. It can also identify and plot extreme cases within the sample.
Box and Whiskers:
The box plot shows a box encased by two outer lines known as whiskers. The box represents the middle 50% of the data sample – half of all cases are contained within it. The remaining 50% of the sample is contained within the areas between the box and the whiskers, with some exceptions (these exceptions are called outliers and they will be discussed more extensively later). For example, consider a sample of 100 IQ scores. The bottom 25% of the scores would be represented by the space between the lower whisker and the box, the middle 50% would be within the box, and the remaining 25% would be contained between the box and the upper whisker.
Inside the box, there is a single line. This line represents the median, which is the middle value of the entire sample. Trace this line back to the axis to derive its value. The location of the median line can also suggest skewness in the distribution if it is noticeably shifted away from the center.
The location of the box within the whiskers can provide insight on the normality of the sample’s distribution. When the box is not centered between the whiskers, the sample may be positively or negatively skewed. If the box is shifted significantly to the low end, it is positively skewed; if the box is shifted significantly to the high end, it is negatively skewed.
The size of the box can provide an estimate of the kurtosis – the peakedness – of the distribution. A very thin box relative to the whiskers indicates that a very high number of cases are contained within a very small segment of the sample. This signifies a distribution with a thinner peak. A wider box relative to the whiskers indicates a wider peak. The wider the box, the more U-shaped the distribution becomes.
Outliers are not present in every box plot. When they are present, they are found in the form of points, circles, or asterisks outside of the boundaries of the whiskers. These are extreme values that deviate significantly from the rest of the sample and they can exist above or below the whiskers of the box plot.