How to read a box plot
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.
Median Line:
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.
Box Position:
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 (right) skewed; if the box is shifted significantly to the high end, it is negatively (left) skewed.
negative skew: the mass of the distribution is concentrated on the right . It has relatively few low values. The distribution is said to be left-skewed, or skewed to the left.]Example (observations): 1,1001,1002,1003.
positive skew: The mass of the distribution is concentrated on the left . It has relatively few high values. The distribution is said to be right-skewed, right-tailed, or skewed to the right. Example (observations): 1,2,3,1000.
If Q3-m > Q1-m then it’s Positive or Right Skewness
If Q3-m < Q1-m then it’s Positive or Left Skewness
The examples below show some common patterns.
2 / 4 / 6 / 8 / 10 / 12 / 14 / 16/
2 / 4 / 6 / 8 / 10 / 12 / 14 / 16
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2 / 4 / 6 / 8 / 10 / 12 / 14 / 16
Skewed right / Symmetric / Skewed left
Each of the above boxplots illustrates a different skewness pattern. If most of the observations are concentrated on the low end of the scale, the distribution is skewed right; and vice versa. If a distribution is symmetric, the observations will be evenly split at the median, as shown above in the middle figure.
Box Size:
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:
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.