Statistics from a Large Sample

Statistics from a Large Sample

What is this problem about?

The Statistics from a Large Sample coding problem involves processing a compressed representation of a large dataset. Instead of a list of individual numbers, you are given a frequency array where count[i] represents how many times the number i appears in the sample. You need to calculate five statistical metrics: the minimum, maximum, mean, median, and mode of the dataset.

Why is this asked in interviews?

This problem is asked by companies like Microsoft to test a candidate's ability to work with large datasets efficiently. It assesses your understanding of basic statistics and your ability to translate statistical definitions into code when the data is not in a standard "flat" list format. It also checks for precision handling when dealing with floating-point numbers for the mean and median.

Algorithmic pattern used

The primary pattern is simple Array traversal and Math. Since the range of numbers is small (typically 0-255), we can iterate through the frequency array to find the statistics.

• Min/Max: First and last indices with non-zero counts.
• Mean: Total sum (index * count) divided by the total number of elements.
• Mode: The index with the highest count.
• Median: Finding the middle element(s) by keeping a running count as you iterate through the frequency array.

Example explanation (use your own example)

Suppose our frequency array is [0, 2, 1, 3] for numbers 0 to 3.

• Counts: 0:0, 1:2, 2:1, 3:3. Total elements = 6.
• Min = 1, Max = 3.
• Mean = $(0\cdot 0 + 1\cdot 2 + 2\cdot 1 + 3\cdot 3) / 6 = (0+2+2+9) / 6 = 13/6 \approx 2.16667$.
• Mode = 3 (appears 3 times).
• Median: Since there are 6 elements, we need the average of the 3rd and 4th elements. The 1st and 2nd are 1s, the 3rd is a 2, the 4th, 5th, and 6th are 3s. Median = $(2+3)/2 = 2.5$.

Common mistakes candidates make

• Integer division: Using integer division for the mean when a float is required.
• Median calculation: Incorrectly finding the middle elements, especially when the total count is even.
• Memory inefficiency: Trying to "expand" the frequency array into a full list, which can lead to memory overflow for large samples.
• Precision: Not handling enough decimal places as required by the problem statement.

Interview preparation tip

For Probability and Statistics interview pattern problems, always clarify the expected precision for floating-point answers. Practice calculating medians on frequency tables, as that is usually the most error-prone part of this Statistics from a Large Sample interview question.