How to calculate statistics with NumPy

Measurements often need more than a single average before their pattern becomes clear. A median limits the influence of extreme values, standard deviation describes spread, and percentiles show how observations are distributed through a range.

A two-dimensional NumPy array can be reduced as one flattened dataset or along a selected axis. Using axis=0 summarizes each column across all rows, while axis=1 summarizes the values within each row.

Missing values and degrees of freedom change the meaning of a summary. np.nanmean() excludes NaN entries from each mean, while std() uses ddof=0 for a population calculation and ddof=1 for the common sample calculation.

1. Create statistics-calculate.py with the score matrix and one missing-value copy.

   statistics-calculate.py

   import numpy as np
    
   np.set_printoptions(precision=2, suppress=True)
    
   scores = np.array(
       [
           [72.0, 75.0, 79.0],
           [80.0, 82.0, 88.0],
           [68.0, 74.0, 77.0],
           [88.0, 93.0, 96.0],
       ]
   )
    
   scores_with_missing = scores.copy()
   scores_with_missing[1, 2] = np.nan

   The scores rows represent records and the columns represent three comparable measurements. The copied array keeps the complete data available for ordinary reductions.

2. Append whole-array center and spread calculations to statistics-calculate.py.

   statistics-calculate.py

   print("overall mean:", scores.mean())
   print("overall median:", np.median(scores))
   print("population std:", round(float(scores.std()), 2))
   print("sample std:", round(float(scores.std(ddof=1)), 2))

   scores.std() divides by N through its default ddof=0. For sample data, ddof=1 changes the divisor to N - 1.

3. Append column, percentile, and NaN-aware calculations to statistics-calculate.py.

   statistics-calculate.py

   print("column means:", scores.mean(axis=0))
   print("column quartiles:")
   print(np.percentile(scores, [25, 50, 75], axis=0))
   print("row means with NaN ignored:", np.nanmean(scores_with_missing, axis=1))
   print("ordinary mean with NaN:", np.mean(scores_with_missing))

   The percentile rows represent the 25th, 50th, and 75th percentiles for each column. An ordinary mean propagates NaN, whereas np.nanmean() calculates from the remaining values in each row.

4. Run statistics-calculate.py to confirm that NumPy returns each summary from the score matrix.

   $ python3 statistics-calculate.py
   overall mean: 81.0
   overall median: 79.5
   population std: 8.29
   sample std: 8.66
   column means: [77. 81. 85.]
   column quartiles:
   [[71.   74.75 78.5 ]
    [76.   78.5  83.5 ]
    [82.   84.75 90.  ]]
   row means with NaN ignored: [75.33 81.   73.   92.33]
   ordinary mean with NaN: nan

   The scalar values summarize all 12 scores, the three-element rows retain the selected axis, and the final nan confirms that the ordinary reduction does not ignore the missing entry.