Normalized histograms in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of normalized histogram with density=True

What is the output of the following code snippet that plots a normalized histogram using matplotlib?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(0)
data = np.random.normal(loc=0, scale=1, size=1000)

counts, bins, patches = plt.hist(data, bins=10, density=True)
plt.close()
print(counts.round(3))

A [0.04 0.07 0.12 0.18 0.22 0.19 0.12 0.05 0.01 0. ]

B [0.04 0.07 0.12 0.18 0.22 0.19 0.12 0.05 0.01 0.01]

C [40. 70. 120. 180. 220. 190. 120. 50. 10. 0.]

D [0.004 0.007 0.012 0.018 0.022 0.019 0.012 0.005 0.001 0. ]

💡 Hint

Remember that density=True scales counts so the area sums to 1, not the counts themselves.

When density=True, the histogram counts are normalized so that the total area under the histogram equals 1. The counts array represents the height of each bin's bar, not the raw counts. The values are roughly between 0 and 0.25 here, matching option A.

❓ data_output

intermediate

Number of bins with non-zero density in normalized histogram

Given the following code that creates a normalized histogram, how many bins have a non-zero density value?

Matplotlib

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(1)
data = np.random.uniform(0, 5, 500)
counts, bins, _ = plt.hist(data, bins=5, density=True)
plt.close()
print(sum(counts > 0))

A 4

B 5

C 3

D 0

💡 Hint

Uniform data over the range 0 to 5 with 5 bins should fill all bins.

Since the data is uniformly distributed between 0 and 5 and the bins cover this range evenly, all 5 bins will have some data points, so all bins have non-zero density.

❓ visualization

advanced

Effect of density parameter on histogram area

Which histogram plot correctly shows a normalized histogram where the total area under the bars sums to 1?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(2)
data = np.random.exponential(scale=1.0, size=1000)

plt.figure(figsize=(10,4))
plt.subplot(1,2,1)
plt.hist(data, bins=20, density=False)
plt.title('Histogram with density=False')

plt.subplot(1,2,2)
plt.hist(data, bins=20, density=True)
plt.title('Histogram with density=True')
plt.close()

A Both plots area sum to 1

B Both plots area sum to 1000

C Left plot area sums to 1, right plot area sums to 1000

D Left plot area sums to 1000, right plot area sums to 1

💡 Hint

density=True normalizes the histogram so the area sums to 1.

When density=False, the histogram shows raw counts, so the total area equals the number of samples (1000). When density=True, the histogram is normalized so the total area sums to 1.

🔧 Debug

advanced

Identify the error in normalized histogram code

What error will this code raise when trying to plot a normalized histogram?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(100)
plt.hist(data, bins=10, density='True')
plt.show()

A TypeError: 'str' object cannot be interpreted as a boolean

B ValueError: bins must be an integer or sequence

C No error, plot shows correctly

D NameError: name 'True' is not defined

💡 Hint

Check the type of the density parameter value.

The density parameter expects a boolean True or False, not the string 'True'. Passing a string causes a TypeError.

🚀 Application

expert

Calculate probability from normalized histogram bins

Given a normalized histogram with bin edges [0, 1, 2, 3] and densities [0.2, 0.3, 0.5], what is the probability that a random value falls between 1 and 3?

A 0.3

B 0.5

C 0.8

D 1.0

💡 Hint

Probability for a bin = density * bin width. Sum probabilities for bins between 1 and 3.

Bin widths are 1 each. Probability between 1 and 3 is sum of densities * widths for bins [1-2] and [2-3]: (0.3*1) + (0.5*1) = 0.8.