Understanding the box and whisker plot

Box and whisker plot definition:
The basic assumption in statistics is that a set of data has a central tendency. That means the number of the data are distributed around some central value. The box of the box-whisker plot takes care of the middle half observations of the data. So we can define the box-whisker plot as a diagram that represents the tendency of data to centre on the median.

Box and whisker plot examples:
The following pictures show box and whisker plot of various data sets.

Shown above is a box-whisker plot of weight in pounds of players.

Shown below is a box- whisker plot of the length of fish in a particular lake:

From the plot we can see that the median length is 12 cm. The smallest fish has a length of 5 cm, the longest fish is 20 cm long. Most of the fishes lie between 8.5 to 14 cm in length, where 8.5 is the lower quartile and 14 cm is the upper quartile.

How to make a box and whisker plot:
Step 1: Arrange the data in ascending order from the lowest to highest value.

Step 2: Find the median of the data. For a data of n observations, median = ((n+1)/2)th observation if n is even and if n is odd then median = average of (n/2)th and ((n+2)/2)th observation. So if number of observations = 11 then (11+1)/2 = 12/2 = 6th observation is the median. But if number of observations is 14, then average of 14/2 = 7th and (14+2)/2 = 16/2 = 8th observation would be the median.

Step 3: The median that we found above has now divided the data into two halves. Now to further divide each of the half into two quarters, we need the 1st and the 3rd quartile values. Suppose the median is the mth observation. Then the middle value between the 1st and the mth observation would be the 1st quartile and the middle value between the mth and the last observation would be the 3rd quartile. They are denoted by Q1 and Q3.

Step 4: Now  you have these three values, Q1, M (= median) and Q3. We also have the lowest and the highest observation, X1 and Xn. So we now have 5 points. We make a number line using suitable scale and mark these 5 points and draw a box around the Q1 to Q3. That is our box and whisker plot.