30. Statistics for Analysts

30.1 Descriptive Statistics with Functions: Centre, Spread and Shape

By Ravindra Bagale · Last updated: 7 October 2026

Example first. Ravina's manager asks: "How fast do we deliver in Pune?" She has the delivery minutes of 20 orders. The average is 13.5 minutes, but 19 of the 20 orders took 17 minutes or less. One order (BLK-5020) took 41 minutes because the rider was stuck in rain. The median is 12 minutes. Which number is "the" answer? This lesson shows the functions that describe a column of numbers: where the centre is, how spread out the values are, and what shape they have, and when to trust each one.

First look at the data (before → after):

Expected result — Summary of 20 delivery times

=AVERAGE(B2:B21)   =MEDIAN(B2:B21)   =MODE.SNGL(B2:B21)
=STDEV.S(B2:B21)   =QUARTILE.INC(B2:B21,1)   =QUARTILE.INC(B2:B21,3)
=SKEW(B2:B21)   =KURT(B2:B21)

The data: 20 delivery times (minutes), Pune, fictional

Every descriptive function on one sheet

Every number on this page was computed with Excel's documented formulas and re-checked twice: in LibreOffice Calc 25.2 with the same formulas, and in Python with scipy and statsmodels.

Mean or median? Use the mean when the values are roughly symmetric and every value matters for a total (for example, average basket value to plan revenue). Use the median when a few extreme values exist and you want the "typical" case (delivery time, salary, house price). Here the mean of the other 19 orders is 12.05; adding the single 41-minute order moves the mean to 13.5 but the median stays at 12. A good report shows both, plus the 90th percentile: "90% of orders arrive within 16.1 minutes."

STDEV.S or STDEV.P? STDEV.S divides by n − 1 and is the right choice when your 20 orders are a sample of many more orders (almost always the case in analysis). STDEV.P divides by n and is only for the complete population, for example the marks of every student in one class. With 20 values the two differ a little (6.8863 vs 6.7119); with 5 values the difference is big. The old functions STDEV and STDEVP still work and equal STDEV.S and STDEV.P.

How to read standard deviation. "Mean 13.5, standard deviation 6.9" says a typical order is about 7 minutes away from the average. But this number is inflated by one outlier: without BLK-5020 the standard deviation is only 2.41. When skewness is far from 0 (here 3.647), prefer the median and the interquartile range (10.75 to 14, so the middle half of orders takes between 10.75 and 14 minutes).

Quartile versions. QUARTILE.INC and PERCENTILE.INC include the minimum and maximum as the 0% and 100% points (the same method as the old QUARTILE function). QUARTILE.EXC and PERCENTILE.EXC use a slightly different method and give a Q1 of 10.25 on this data. Pick one method and use it in every report; pandas describe() (lesson 29.4) matches the .INC versions.

Microsoft sources (checked 7 October 2026): STDEV.S function.

Practice task (try it before you open the answer):

1. Remove BLK-5020 (41 minutes) and recalculate the mean, median and STDEV.S of the other 19 orders.
2. Which measure changed the most, and why?
3. Write the 90th percentile of the 19 orders with PERCENTILE.INC.