Stop 04 · Statistics for AnalystsTopics · 1/11

Descriptive Statistics (Mean, Median, Mode, Std Dev)

In short

"Average salary in our class is ₹18 lakh!" Then you learn one student got ₹1.5 crore. Knowing mean vs median stops you being fooled, and stops you fooling others.

The basic summary numbers for any dataset — mean and median describe the center (and disagree when data is skewed), mode is the most frequent value, and standard deviation describes spread.

The jaadu holds a measuring tape beside a row of creatures lined up shortest to tallest.

Think of it like this

Lining up by height

Line up your hostel wing by height. The middle person is the median. Add one 7-foot basketball player and the mean jumps, but the median barely moves. Standard deviation is how spread out the line is: all similar, or wildly different.

Watch it happen

One big salary changes the mean

1/5Five placement offers in lakhs per year: 6, 7, 7, 8, 9.

The big ideas

What you need to know

Mean: the balance point

Sum divided by count. Great for symmetric data, easily dragged by extreme values.

Median: the middle value

Sort and take the middle. Resistant to outliers, so better for incomes, house prices and delivery times.

Mode: the most common

Useful for categories, like the most popular pizza size. A dataset can have more than one mode.

Standard deviation: the spread

Roughly how far values typically sit from the mean. Small means consistent, large means all over the place.

See it in code

Walk through the code

excel

1=AVERAGE(B2:B101)2=MEDIAN(B2:B101)3=MODE.SNGL(B2:B101)4=STDEV.S(B2:B101)5=QUARTILE.INC(B2:B101, 3) - QUARTILE.INC(B2:B101, 1)

1/3Centre: mean, median, mode. If mean and median differ a lot, the data is skewed.

The five numbers to check first on any numeric column. STDEV.S is for a sample, which is almost always what you have.

Save yourself the pain

Common mistakes

Oops

Reporting average delivery time when a few orders took hours.

Do this instead

Report the median and maybe the 90th percentile. They describe a typical customer far better.

Oops

Quoting a mean with no sense of spread.

Do this instead

Add standard deviation or a range. 'Average 30 min, most between 22 and 38' tells a fuller story.

Your mission

Describe your own data

~20 min

Quick check

House prices in an area are heavily skewed by a few mansions. Which number best describes a typical house?

Go deeper

1Calculate all 4 by hand on a small dataset before using a tool.
2Learn why median is more robust to outliers than mean.
3Find a real dataset where mean and median differ noticeably, and explain why.