Overlaying boxplots on the relative bin of a histogram

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Taking the dataset 'tip' as an example

total_bill tip smoker day time size
16.99 1.01 No Sun Dinner 2
10.34 1.66 No Sun Dinner 3
21.01 3.50 No Sun Dinner 3
23.68 3.31 No Sun Dinner 2
24.59 3.61 No Sun Dinner 4

what I'm trying to do is represent the distribution of the variable 'total_bill' and relate each of its bins to the distribution of the variable 'tip' linked to it. In this example, this graph is meant to answer the question: "What is the distribution of tips left by customers as a function of the bill they paid?"

I have more or less achieved the graph I wanted to obtain (but there is a problem. At the end I explain what it is).
And the procedure I adopted is this:

  1. Dividing 'total_bill' into bins.

    tips['bins_total_bill'] = pd.cut(tips.total_bill, 10)
tips.head()
    total_bill tip smoker day time size bins_total_bill
    16.99 1.01 No Sun Dinner 2 (12.618, 17.392]
    10.34 1.66 No Sun Dinner 3 (7.844, 12.618]
    21.01 3.50 No Sun Dinner 3 (17.392, 22.166]
    23.68 3.31 No Sun Dinner 2 (22.166, 26.94]
    24.59 3.61 No Sun Dinner 4 (22.166, 26.94]

  2. Creation of a pd.Series with:
    Index: pd.interval of total_cost bins
    Values: n° of occurrences

    s = tips['bins_total_bill'].value_counts(sort=False)
s

(3.022, 7.844]       7
(7.844, 12.618]     42
(12.618, 17.392]    68
(17.392, 22.166]    51
(22.166, 26.94]     31
(26.94, 31.714]     19
(31.714, 36.488]    12
(36.488, 41.262]     7
(41.262, 46.036]     3
(46.036, 50.81]      4
Name: bins_total_bill, dtype: int64

  1. Combine barplot and poxplot together

    fig, ax1 = plt.subplots(dpi=200)
ax2 = ax1.twinx()

sns.barplot(ax=ax1, x = s.index, y = s.values)
sns.boxplot(ax=ax2, x='bins_total_bill', y='tip', data=tips)
sns.stripplot(ax=ax2, x='bins_total_bill', y='tip', data=tips, size=5, color="yellow", edgecolor='red', linewidth=0.3)

#Title and axis labels
ax1.tick_params(axis='x', rotation=90)
ax1.set_ylabel('Number of bills')
ax2.set_ylabel('Tips [$]')
ax1.set_xlabel("Mid value of total_bill bins [$]")
ax1.set_title("Tips ~ Total_bill distribution")

#Reference lines average(tip) + add yticks + Legend
avg_tip = np.mean(tips.tip)
ax2.axhline(y=avg_tip, color='red', linestyle="--", label="avg tip")
ax2.set_yticks(list(ax2.get_yticks() + avg_tip))
ax2.legend(loc='best')

#Set labels axis x
ax1.set_xticklabels(list(map(lambda s: round(s.mid,2), s.index)))

    barplot and poxplot together

It has to be said that this graph has a problem! As the x-axis is categorical, I cannot, for example, add a vertical line at the mean value of 'total_bill'.

How can I fix this to get the correct result? I also wonder if there is a correct and more streamlined approach than the one I have adopted.

pandas seaborn matplotlib
1 Answers

I thought of this method, which is more compact than the previous one (it can probably be done better) and overcomes the problem of scaling on the x-axis.

  1. I split 'total_bill' into bins and add the column to Df

    tips['bins_total_bill'] = pd.cut(tips.total_bill, 10)

  2. Group column 'tip' by previously created bins

    obj_gby_tips = tips.groupby('bins_total_bill')['tip']
gby_tip = dict(list(obj_gby_tips))

  3. Create dictionary with:
    keys: midpoint of each bins interval
    values: gby tips for each interval

    mid_total_bill_bins = list(map(lambda bins: bins.mid, list(gby_tip.keys())))
gby_tips = gby_tip.values()

tip_gby_total_bill_bins = dict(zip(mid_total_bill_bins, gby_tips))

  4. Create chart by passing to each rectangle of the boxplot the centroid of each respective bins

    fig, ax1 = plt.subplots(dpi=200)
ax2 = ax1.twinx()

bp_values = list(tip_gby_total_bill_bins.values())
bp_pos = list(tip_gby_total_bill_bins.keys())

l1 = sns.histplot(tips.total_bill, bins=10, ax=ax1)
l2 = ax2.boxplot(bp_values, positions=bp_pos, manage_ticks=False, patch_artist=True, widths=2)

#Average tips as hline
avg_tip = np.mean(tips.tip)
ax2.axhline(y=avg_tip, color='red', linestyle="--", label="avg tip")
ax2.set_yticks(list(ax2.get_yticks() + avg_tip)) #add value of avg(tip) to y-axis

#Average total_bill as vline
avg_total_bill=np.mean(tips.total_bill)
ax1.axvline(x=avg_total_bill, color='orange', linestyle="--", label="avg tot_bill")

then the result.

Tips ~ Total_bill distribution

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