Mean vs median vs mode: which one to use

You

Alex, help me work through “Typical value: mean, median, mode” step by step.

Alex Tutor

It's Monday stand-up at CatChow, a small online shop selling cat food, treats and litter. The marketing lead is planning a free-shipping offer and asks one simple question: what does a typical order look like?

You open last week's orders: 20 of them, from $18 to $284. Nobody wants to hear twenty numbers, so you need one number that stands for all of them. Statisticians call such a number a measure of central tendency. There are several, and they can give very different answers from the same data. Choosing the right one is a product decision, not a formality.

In this lesson you'll learn four of them (the mean, the median, the mode and the trimmed mean), plus a trap that catches almost every dashboard: averaging averages. You can download the week of orders below and follow along in Google Sheets or Excel.

Alex Tutor

Dataset · 20 rows

CatChow orders, 14–20 September

20 orders placed in one week. Synthetic data made for this course.

Download CSV

Columns
order_id: Order number
order_date: Date the order was placed (YYYY-MM-DD)
order_value: Order value, USD

Data

order_id	order_date	order_value
CC-1041	2026-09-14	48
CC-1042	2026-09-14	40
CC-1043	2026-09-14	34
CC-1044	2026-09-15	48
CC-1045	2026-09-15	28

Show 15 more rows

CC-1046	2026-09-15	28
CC-1047	2026-09-16	284
CC-1048	2026-09-16	24
CC-1049	2026-09-17	38
CC-1050	2026-09-17	18
CC-1051	2026-09-17	31
CC-1052	2026-09-18	28
CC-1053	2026-09-18	45
CC-1054	2026-09-18	30
CC-1055	2026-09-18	36
CC-1056	2026-09-19	24
CC-1057	2026-09-19	22
CC-1058	2026-09-19	35
CC-1059	2026-09-20	26
CC-1060	2026-09-20	33

Alex Tutor

Question 1

CatChow's product pages usually load in 1–2 seconds, but about 3% of loads hit a 30-second timeout. You want one number that describes what a typical visitor experiences. Which do you report?

Choose one answerThe mean load timeThe median load timeThe mode of load timesThe longest load time

Alex Tutor

The mean (arithmetic mean) is what most people call "the average": add up all the values and divide by how many there are. Last week CatChow took $900 across 20 orders, so the mean order value is $900 / 20 = $45.

In e-commerce this number has its own name: average order value (AOV). It is the mean by definition, total revenue divided by the number of orders.

The mean has one great strength. It is tied to the total: mean × count = total, always. If you expect 400 orders next month and the mean stays at $45, you can forecast $18,000 of revenue. No other measure in this lesson lets you do that.

Alex Tutor

\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{1}{n}\sum_{i=1}^{n} x_i

The mean: the sum of all n values divided by n. The bar over x reads "x-bar".

Alex Tutor

Question 2

If the mean order value is higher than the median, then most orders are above the mean.

TrueFalse

Now look at the orders themselves. 16 of the 20 orders are below $45. How can the "typical" order be bigger than almost every real order?

Scroll the file and you'll find order CC-1047: $284. A local cat shelter stocked up for the month. That single order adds $284 to the total, and because the mean shares the total equally, it lifts every order's "fair share" by about $12.6. The mean answers "how much would each order be if they were all equal?", and that is not the same question as "what does a normal order look like?"

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The median ignores the sizes of the extremes and only asks about order. Sort the values from smallest to largest and take the one in the middle. Half of the orders are smaller, half are larger.

With an odd number of values there is exactly one middle value: for 7 values it is the 4th. With an even number there are two, so you average them. Our 20 sorted orders have 31 in 10th place and 33 in 11th place, so the median is

(31 + 33) / 2 = 32

dollars.

In Sheets or Excel: =MEDIAN(C2:C21). By hand, the only real work is sorting.

Alex Tutor

Question 3

Match each question to the measure that answers it best.

Pick an answer for each row. Choosing an answer that is already used moves it to this row.

Which flavour do customers pick most often?
Choose an answer
How many days does a typical new user take to place a first order? (A few take almost a year.)
Choose an answer
How much revenue will 400 orders bring next month?
Choose an answer
What is the overall conversion rate across five countries with very different traffic?
Choose an answer

Alex Tutor

\operatorname{Me} = \begin{cases} x_{(k+1)}, & n = 2k + 1 \\[6pt] \dfrac{x_{(k)} + x_{(k+1)}}{2}, & n = 2k \end{cases}

Values are sorted from smallest to largest; x₍ₖ₎ is the k-th of them. Top line: odd n; bottom line: even n.

Alex Tutor

Last week's orders by valueMost orders sit between 20 USD and 40 USD. One bulk order of 284 USD sits far to the right and drags the mean up to 45 USD, while the median stays at 32 USD.

Chart data

Order value, USD	Orders
10–19	1
20–29	7
30–39	7
40–49	4
50–279	0

Show 1 more row

280–289

1

Alex Tutor

Question 4

Download the dataset CatChow orders, 14–20 September. What is the median order value?

Your answer

Units: USD, e.g. 32.5

Alex Tutor

Here is the clearest way to see the difference. Remove the shelter's order and recompute:

	All 20 orders	Without CC-1047
Mean	$45.00	$32.42
Median	$32	$31

One order out of twenty moved the mean by more than $12 but moved the median by $1. We say the median is robust: a few extreme values barely affect it. The mean is sensitive: it reacts to every single value, including the weird ones.

Neither behaviour is "better". If the question is how much revenue did we make?, the shelter's $284 is real money and belongs in the answer, so you want the mean. If the question is what does a normal customer put in the basket?, the shelter is not a normal customer, so you want the median.

Alex Tutor

Question 5

In the same dataset, remove the shelter's bulk order CC-1047 ($284). What is the mean of the remaining 19 orders? Round to cents.

Your answer

Units: USD, e.g. 32.5

Alex Tutor

The mode is the value that appears most often. Among last week's orders, $28 appears three times, more than any other value, so the mode is $28.

For money and time, the mode is usually the least useful measure. With precise values (like $31.47) almost nothing repeats, and a tiny change in the data can move the mode somewhere else entirely. Here $24 and $48 each appear twice, only one order behind.

The mode shines with categories, where mean and median make no sense at all. What is the most popular flavour, salmon or chicken? Which plan do most subscribers choose? What rating do users give most often? You can't average "salmon" and "chicken", but you can count them. The mode is the only measure of central tendency that works for categories.

Watch out for data with two modes. If a histogram of basket sizes has one peak around $25 and another around $120, you probably have two different kinds of customers (households and, say, shelters or cat cafés). Any single "typical value" would describe neither group. That's a hint to segment, not to average.

Alex Tutor

Sometimes you want something that behaves like a mean but doesn't let a handful of extremes run the show. The trimmed mean does exactly that: sort the data, drop a fixed share from each end (often 5–10%), and take the mean of what's left.

With a 10% trim on 20 orders, you drop 2 from the bottom ($18, $22) and 2 from the top ($48, $284). The remaining 16 orders add up to $528, so the trimmed mean is $528 / 16 = $33. That's close to the median, but it still uses the actual values of 16 orders instead of just the middle two.

You have met this idea before: in some judged sports the highest and lowest scores are thrown away before averaging, so that one overly generous or harsh judge can't swing the result. In Sheets or Excel: =TRIMMEAN(C2:C21, 0.2). Note that the function takes the total share to remove, so 0.2 means 10% from each end.

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Question 6

Which statements about the mean are true? Select all that apply.

Choose all that applyMean × number of values = totalIt is always one of the actual values in the dataA single extreme value can move it a lotIt works for categories such as cat-food flavoursIt uses every value in the data

Alex Tutor

\bar{x}_{[k]} = \frac{1}{n - 2k}\sum_{i=k+1}^{n-k} x_{(i)}

Trimmed mean: sort the values, drop k from each end, average the remaining n − 2k.

Alex Tutor

One more mean, because it causes real mistakes in product reviews. Suppose CatChow's checkout conversion last month was 2% on mobile (8,000 sessions) and 5% on desktop (2,000 sessions). What is the overall conversion rate?

The tempting answer is

(2\% + 5\%) / 2 = 3.5\%

. It's wrong. Mobile had four times the traffic, so it should count four times as much. Count the orders instead:

8{,}000 \times 0.02 = 160

on mobile plus

2{,}000 \times 0.05 = 100

on desktop gives 260 orders from 10,000 sessions, which is 2.6%.

This is a weighted mean: each group's value counts in proportion to its size. Whenever you combine rates or averages from segments (by channel, country, device, cohort), weight them by the segment's size, or simply go back to the raw totals and divide.

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Question 7Short answer · AI-checked task

A weekly report says: "Average order value jumped from $38 to $52 this week!" Before celebrating, what would you check, and why? Answer in 2–4 sentences.

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Alex Tutor

\bar{x}_w = \frac{\sum_{i} w_i x_i}{\sum_{i} w_i}

Weighted mean: multiply each value by its weight (e.g. sessions), add up, divide by the total weight.

Alex Tutor

Your question	Use	Why
How much revenue will N orders bring?	Mean	Only the mean links to totals
What does a typical order or user look like?	Median	Robust to a few extreme values
Which category is most popular?	Mode	The only option for categories
A mean-like number that resists a few freak values	Trimmed mean	Keeps most of the data, drops the extremes
Combining rates across segments of different size	Weighted mean	Big segments must count more

A habit worth building: whenever someone shows you "the average", ask which average, and computed over what? Most tools default to the mean, and most product data (order values, session lengths, revenue per user) has a long right tail. In the next lessons you'll learn to measure how spread out the data is, and how to spot and handle the extreme values that made our mean misbehave.

Alex Tutor

Question 8Case · AI-checked task

What free-shipping threshold would you recommend, and why? Use numbers from the dataset.

CatChow wants to introduce free shipping above a minimum order value. The goal is to nudge a typical customer to add one more item to the basket, while keeping shipping costs under control.

The marketing lead proposes a threshold of $45, "because that's our average order". You have last week's 20 orders (dataset CatChow orders, 14–20 September). Write a short recommendation for her: which threshold you'd pick, how you got there, and what you'd watch out for.

Dataset for this task: CatChow orders, 14–20 September

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Alex Tutor

That’s the lesson. You answered every task — nicely done.

Next lesson: Spread: range, SD and quartiles