Python Statistics Collector

This challenge involves building a Python class that can efficiently collect and compute various statistical measures from a stream of numerical data. This is a common task in data analysis, machine learning, and real-time monitoring systems where understanding the distribution and central tendencies of data is crucial.

Problem Description

You need to create a Python class named StatisticsCollector. This class should be able to:

1. Accept numerical data: It should have a method to add individual numerical values to its collection.
2. Calculate key statistics: It should provide methods to compute and return:
   • The count of data points collected.
   • The sum of all data points.
   • The mean (average) of the data points.
   • The minimum value observed.
   • The maximum value observed.
   • The median of the data points.
   • The variance of the data points.
   • The standard deviation of the data points.
3. Handle edge cases: Consider scenarios where no data has been added or when calculations involving zero variance occur.

Examples

Example 1:

collector = StatisticsCollector()
collector.add_data(10)
collector.add_data(20)
collector.add_data(30)
collector.add_data(40)
collector.add_data(50)

print(f"Count: {collector.count()}")
print(f"Sum: {collector.sum()}")
print(f"Mean: {collector.mean()}")
print(f"Min: {collector.min()}")
print(f"Max: {collector.max()}")
print(f"Median: {collector.median()}")
print(f"Variance: {collector.variance()}")
print(f"Standard Deviation: {collector.std_dev()}")

Output:

Count: 5
Sum: 150
Mean: 30.0
Min: 10
Max: 50
Median: 30
Variance: 250.0
Standard Deviation: 15.811388300841896

Explanation: The collector processes the numbers 10, 20, 30, 40, and 50, calculating the requested statistics. The median is 30 because it's the middle element in the sorted list. Variance and standard deviation are calculated using the population formulas.

Example 2:

collector = StatisticsCollector()
collector.add_data(5)
collector.add_data(5)
collector.add_data(5)

print(f"Mean: {collector.mean()}")
print(f"Variance: {collector.variance()}")

Output:

Mean: 5.0
Variance: 0.0

Explanation: When all data points are the same, the mean is that value, and the variance/standard deviation is zero.

Example 3: (Edge Case: Empty Collection)

collector = StatisticsCollector()

print(f"Count: {collector.count()}")
print(f"Mean: {collector.mean()}") # Should handle division by zero
print(f"Min: {collector.min()}")   # Should handle no data
print(f"Max: {collector.max()}")   # Should handle no data

Output:

Count: 0
Mean: 0.0
Min: None
Max: None

Explanation: If no data is added, the count is 0. The mean should return 0.0 (or None as an alternative, but 0.0 is specified here for simplicity), and min/max should return None as there's no data to compare.

Constraints

• The add_data method will only receive numeric types (integers or floats).
• The StatisticsCollector should maintain its internal state efficiently, especially if dealing with a large number of data points over time.
• Calculations for variance and standard deviation should use the population formulas (dividing by N, not N-1).

Notes

• You will need to store the data points to calculate the median, variance, and standard deviation. Consider how you will store this data.
• For median calculation, you'll need to sort the data.
• Be mindful of potential division by zero errors when calculating the mean, variance, and standard deviation, especially when the collection is empty.
• Consider what return values make the most sense for statistics when no data is available (e.g., None for min/max, 0.0 for mean, and 0.0 for variance/std_dev).
• The variance is the average of the squared differences from the mean. The standard deviation is the square root of the variance.