Outliers and skewed data

You

Alex, help me work through “Outliers and skewed data” step by step.

Alex Tutor

CatChow's growth team is preparing a quarterly review. One slide shows the 90-day spend of new customers: how much each customer who joined in June spent in their first 90 days. The analyst took a random sample of 24 of them (download it below).

The mean is $50. The median is $35. Two-thirds of the customers (16 of 24) spent less than the mean. And one customer, U-5120, spent $240, almost five times the mean.

Someone suggests: "Just delete the top values, they're outliers." Should you? This lesson is about outliers (values far from the rest) and skewed distributions (data with a long tail on one side). They are the norm in product and marketing data, not the exception, and handling them well is one of the most practical skills in this course.

Alex Tutor

Dataset · 24 rows

90-day spend of new CatChow customers

A random sample of 24 customers who joined in June: spend and number of orders in their first 90 days. Synthetic data made for this course.

Download CSV

Columns
customer_id: Customer ID
spend_90d: Total spend in the first 90 days, USD
orders_90d: Number of orders in the first 90 days

Data

customer_id	spend_90d	orders_90d
U-5101	42	2
U-5102	85	3
U-5103	15	1
U-5104	28	1
U-5105	24	1

Show 19 more rows

U-5106	24	1
U-5107	64	2
U-5108	32	1
U-5109	56	2
U-5110	93	3
U-5111	26	1
U-5112	22	1
U-5113	20	1
U-5114	45	2
U-5115	110	4
U-5116	34	1
U-5117	50	2
U-5118	36	1
U-5119	38	1
U-5120	240	12
U-5121	56	2
U-5122	12	1
U-5123	18	1
U-5124	30	1

Alex Tutor

Question 1

Which CatChow metric is most likely to be right-skewed?

Choose one answerRevenue per customer in the first yearWeight of standard 2 kg food bags from the factoryRating given in the app store (1–5 stars)Day of the week an order is placed

Alex Tutor

90-day spend per new customerA long right tail: most customers spent 20–60 USD, a few spent much more, and one spent 240 USD. The tail pulls the mean (50 USD) to the right of the median (35 USD).

Chart data

Spend in 90 days, USD	Customers
0–19	3
20–39	11
40–59	5
60–79	1
80–99	2

Show 3 more rows

100–119	1
120–239	0
240–259	1

Alex Tutor

Question 2

Every outlier should be removed before you analyse the data.

TrueFalse

Alex Tutor

An outlier is an observation that sits far away from the rest of the data. That's a statistical description, not a verdict. Before deciding what to do, ask why the value is so far out. In practice there are three very different reasons:

It's an error. A test order placed by a developer, a price typed as $2,990 instead of $29.90, revenue recorded in the wrong currency, a bot that added 400 items to a basket. These values describe nothing real. Fix or remove them, and write down that you did.
It's a genuine extreme. A real customer who really loves your product and orders a lot. The value is correct; it's just rare. Deleting it means pretending your best customers don't exist.
It's from a different population. Look at U-5120 again: $240 over 12 orders in 90 days, while almost everyone else placed 1–3 orders. That pattern suggests a business (a cat café, a shelter, a small reseller) rather than a household. It's real data, but it answers a different question. Analyse it as a separate segment rather than mixing it with households.

Outliers are information. Sometimes the most important finding in a dataset is the outlier itself: a B2B segment you didn't know you had, or a tracking bug that has been inflating revenue for a month.

Alex Tutor

"Far from the rest" needs a definition, or everyone will draw the line wherever suits their story. The most common rule, proposed by the statistician John Tukey, builds fences from the quartiles you met in the previous lesson:

lower fence: $Q_1 - 1.5 \times \text{IQR}$
upper fence: $Q_3 + 1.5 \times \text{IQR}$

Anything outside the fences is flagged as a potential outlier. For our 24 customers,

Q_1 = 24

and

Q_3 = 56

, so

\text{IQR} = 32

. The upper fence is

56 + 1.5 \times 32 = 104

dollars, and the lower fence is

24 - 48 = -24

dollars (spend can't be negative, so nothing is flagged at the bottom).

Two customers are above $104: U-5115 ($110) and U-5120 ($240). Note that U-5115 spent $110 over 4 orders, which looks like an enthusiastic household rather than a business. The rule flags values for a closer look; it doesn't tell you what they are.

Because the fences are built from quartiles, the outliers themselves can't distort them. That is the rule's biggest strength.

Alex Tutor

Question 3

Match each unusual value to the most sensible action.

Tap an answer, then tap the row it belongs to. You can also drag.

A 0.01 USD order placed by a developer from the office network
A bag of treats recorded at 2,990 USD instead of 29.90 USD
A cat café that orders 12 times a quarter
A household customer who spent 3× the median, in a revenue forecast

Answers left to place

Alex Tutor

x \notin \left[\, Q_1 - \tfrac{3}{2}\,\text{IQR},\;\; Q_3 + \tfrac{3}{2}\,\text{IQR} \,\right]

Tukey's rule: a value outside the fences (3/2 = 1.5) is a potential outlier. Values beyond 3 × IQR are sometimes called extreme outliers.

Alex Tutor

Question 4

A dataset of monthly ad clicks per campaign has $Q_1 = 120$ and $Q_3 = 200$ . Using Tukey's rule, what is the upper fence above which a campaign is flagged as a potential outlier?

Your answer

Units: clicks

Alex Tutor

Another popular rule flags values more than 3 SDs from the mean. It works reasonably well for large, bell-shaped datasets. On small or skewed data it has a nasty flaw: the outliers inflate the very SD you measure them with.

Our sample has a mean of $50 and an SD of about $47.7. U-5120 is

(240 - 50) / 47.7 \approx 3.99

SDs above the mean, so it gets flagged, but only just, and mostly because it is so extreme. U-5115 is only 1.26 SDs above the mean and looks perfectly ordinary.

Now remove U-5120 and recompute: the mean falls to $41.74 and the SD to about $25.7. Suddenly U-5115 is 2.65 SDs out. One extreme value was hiding another. Statisticians call this masking. The IQR rule doesn't suffer from it, which is why it is the better default for everyday product data.

Alex Tutor

Question 5

Using the dataset 90-day spend of new CatChow customers, what share of total 90-day spend (in %) comes from the two customers flagged by the IQR rule? Round to one decimal.

Your answer

Units: %, e.g. 12.5

Alex Tutor

Look at the chart again. The values pile up on the left and trail off in a long tail to the right. That shape is called right-skewed (or positively skewed). In a skewed distribution, the few values in the tail pull the mean towards them, while the median stays with the crowd:

Right skew (long tail to the right): mean > median. Here $50 > $35.
Symmetric: mean ≈ median.
Left skew (long tail to the left): mean < median.

Right skew is everywhere in product and marketing data, because these metrics have a hard floor at zero but no ceiling: revenue per customer, order value, session length, time to first purchase, number of orders, followers per account, ad cost per acquisition. If a metric is "how much" or "how long" and can't go negative, expect a right tail.

Left skew is rarer, but you'll meet it in app-store ratings (most people give 5 stars, with a tail of angry 1s) and in "percent of lesson completed" when most people finish.

The mean-versus-median check is a rule of thumb, not a law; odd shapes can break it. When in doubt, plot the histogram.

Alex Tutor

Question 6

Time to first purchase after sign-up: mean 19 days, median 6 days. What shape does this distribution most likely have?

Choose one answerSymmetricRight-skewed: a long tail of slow buyersLeft-skewed: a long tail of fast buyersIt's impossible to say anything

Alex Tutor

Look before you touch. Open the raw rows. Check dates, IDs, order counts, currency. Is this a bug, a real person, or a different kind of customer?
Fix or remove errors, and log it. Test orders, duplicates and typos go. Write down what you removed and why, so that someone else gets the same numbers.
Choose the summary by the question, not by convenience.
- "How much revenue will the June cohort bring?" Totals need the mean, with the whales included.
- "What does a typical new customer spend?" Use the median (here $35) or a trimmed mean.
- "Is our spend distribution changing?" Track the median and a high percentile (p90) together.
Segment instead of deleting. Pull likely businesses (many orders, large baskets) into their own segment. Households and cafés behave differently and deserve separate metrics.
Use robust tools when extremes aren't the point. Median, IQR, trimmed mean, or capping: replace values above, say, the 99th percentile with the 99th percentile itself (also called winsorising). Capping is common in A/B tests on revenue, where one huge order can otherwise decide the result.
Report with and without. "Mean 90-day spend is $50, or $41.74 excluding one business customer." Two numbers, full honesty, and no one can accuse you of cherry-picking.

Alex Tutor

Question 7Short answer · AI-checked task

Explain in 2–4 sentences why the "more than 3 SDs from the mean" rule can miss outliers in a small, skewed dataset.

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Alex Tutor

Question 8Case · AI-checked task

Which number should go into the acquisition budget, and how do you handle the outliers? Use numbers from the dataset.

CatChow's CEO wants to set the maximum cost per acquired customer for paid ads. Her rule: "We can spend up to one-third of what a new customer brings in their first 90 days." The analyst's slide says average 90-day spend: $50, so the CEO is ready to approve up to $16.67 per customer.

The head of performance marketing objects: "That average is inflated by a couple of weird customers. Use the median, $35." That would cap acquisition cost at $11.67.

Using the dataset 90-day spend of new CatChow customers, write a recommendation: what's going on in the data, which number you'd use for this decision and why, and what you'd do about the outliers.

Dataset for this task: 90-day spend of new CatChow customers

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Alex Tutor

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

Next lesson: Charts: choosing the right one