boxplot using precalculated (summary) statistics

Question

I need to do a boxplot (in Python and matplotlib) but I do not have the original "raw" data. What I have are precalculated values for max, min, mean, median and IQR (normal distribution) but still I'd like to do a boxplot. Of course plotting outliers isn't possible, but beside that I guess all information is there.

I've search all over to find an answer without success. The closest I've come is the same question but for R (which I'm unfamiliar with). See Is it possible to plot a boxplot from previously-calculated statistics easily (in R?)

Collogue

Answer 1

In the old versions, you have to manually do it by changing boxplot elements individually:

Mean=[3.4] #mean
IQR=[3.0,3.9] #inter quantile range
CL=[2.0,5.0] #confidence limit
A=np.random.random(50)
D=plt.boxplot(A) # a simple case with just one variable to boxplot
D['medians'][0].set_ydata(Mean)
D['boxes'][0]._xy[[0,1,4], 1]=IQR[0]
D['boxes'][0]._xy[[2,3],1]=IQR[1]
D['whiskers'][0].set_ydata(np.array([IQR[0], CL[0]]))
D['whiskers'][1].set_ydata(np.array([IQR[1], CL[1]]))
D['caps'][0].set_ydata(np.array([CL[0], CL[0]]))
D['caps'][1].set_ydata(np.array([CL[1], CL[1]]))
_=plt.ylim(np.array(CL)+[-0.1*np.ptp(CL), 0.1*np.ptp(CL)]) #reset the limit

Infract

For people stumbling upon this and despairing about the syntax: There are easier ways to do this now, see the matplotlib documentation: matplotlib.org/gallery/statistics/bxp.html – Linn

Answer 2

Thanks to the comment of @tacaswell I was able to find the required documentation and come up with an example using Matplotlib 1.4.3. However, this example does not automatically scale the figure to the correct size.

import matplotlib.pyplot as plt

item = {}

item["label"] = 'box' # not required
item["mean"] = 5 # not required
item["med"] = 5.5
item["q1"] = 3.5
item["q3"] = 7.5
#item["cilo"] = 5.3 # not required
#item["cihi"] = 5.7 # not required
item["whislo"] = 2.0 # required
item["whishi"] = 8.0 # required
item["fliers"] = [] # required if showfliers=True

stats = [item]

fig, axes = plt.subplots(1, 1)
axes.bxp(stats)
axes.set_title('Default')
y_axis = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
y_values = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
plt.yticks(y_axis, y_values)

Relevant links to the documentation:

• matplotlib.axes.Axes.bxp
• boxplot_stats datastructure
• Boxplot drawer function

Gateway

Answer 3

Referring to the answer of @MKroehnert and Boxplot drawer function at https://matplotlib.org/gallery/statistics/bxp.html, the following could be helpful:

import matplotlib.pyplot as plt

stats = [{
    "label": 'A',  # not required
    "mean":  5,  # not required
    "med": 5.5,
    "q1": 3.5,
    "q3": 7.5,
    # "cilo": 5.3 # not required
    # "cihi": 5.7 # not required
    "whislo": 2.0,  # required
    "whishi": 8.0,  # required
    "fliers": []  # required if showfliers=True
    }]

fs = 10  # fontsize

fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(6, 6), sharey=True)
axes.bxp(stats)
axes.set_title('Boxplot for precalculated statistics', fontsize=fs)
plt.show()

Chance

Just wanted to add to this brilliant answer, if you want to plot multiple boxplots after using a for loop to append multiple stats to a list e.g. (before loop: final_data = list(), within but end of loop: final_data.append(stats)) to then plot them all on one figure, remove the [] around the stats dictionary in this answer. Probably a simple solution but took me a few minutes to figure that out. – Chace