Average, typical, and the odd one out.
Most of an analyst’s statistics is choosing the right summary: the mean or the median, a percentile, a rate, and spotting the values that don’t belong. Here they are on a real shop’s orders and a 5,000-customer table.
- Choose between the mean and the median
- Read percentiles and spread
- Spot impossible values before they mislead you
You need: Nothing: this is where the path starts.
- 1Statistics you use every day
- 2SQL that answers questions
- 3Charts that answer the question
- 4Power BI’s filter context
- 5A/B tests
- 6Guesstimates
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Mean or median?
Predict first
The shop’s 11 orders average ₹1,853. Add one bulk order of ₹49,999 (made up). What happens to the median?
Just show me
It barely moves, from ₹1,899 to ₹1,949, while the mean jumps from ₹1,853 to ₹5,865.
The mean adds everything up, so one big value drags it along. The median is the middle value once they’re sorted, so it only cares about order. Report the median for typical order values, salaries or delivery times, where a few big ones are normal; use the mean when every rupee counts, as in total revenue ÷ orders.
Mean₹1,853Mean, with the bulk order₹5,865Median₹1,899Median, with it₹1,949The shop’s 11 orders (the SQL guide’s example database), then with one made-up ₹49,999 order
Quick check
A report says the average delivery took 3 days, but most took 1. What’s probably going on?
A long tail of late deliveries lifts the mean; the median would say 1 day.
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When most values are zero
Predict first
Complaints in the last 90 days, in the ML guide’s churn table: what’s the median customer’s count?
Just show me
0: 65% of customers made no complaint, so the middle customer made none, while the mean is 0.42, lifted by the few who complained up to 4 times.
When the mean sits well above the median, a long right tail is pulling it, and that tail is often the interesting part. The monthly charge, by contrast, is balanced: mean ₹501, median ₹499. Mostly-zero numbers are often best summed up as a share: “65% made no complaint”.
0 complaints3,2491 complaint1,4202 complaints2953 complaints314 complaints5Customers by complaints in 90 days, out of 5,000 (the ML guide’s churn table, synthetic)
Quick check
Which summary would you report for complaints per customer?
With most values at zero, “65% made no complaint” says more than any single average.
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Percentiles and spread
Predict first
The monthly charge’s 90th percentile is ₹695. What does that mean?
Just show me
90% pay less than about ₹695. The 10th percentile is ₹309, so the middle 80% pay between the two.
Percentiles describe spread in the data’s own units, which a manager understands at once: “most customers pay between ₹309 and ₹695”. The standard deviation (₹150 here) sums up spread in one number; for bell-shaped data, about 95% of values sit within two of them of the mean.
The standard deviation, symbol by symbol
Quick check
Your app’s p95 load time is 4 seconds. What does that tell you?
The 95th percentile: 95% of loads are faster, 5% slower.
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Impossible values
Predict first
Can a customer have a negative monthly charge?
Just show me
Not as a charge, yet 2 customers in the table have one. The table’s code draws charges from a bell curve, and a bell curve has tails; real data has its own versions: typos, test accounts, wrong units.
Before any summary, check the range and the blanks: the minimum, the maximum and the count of missing values (245 charges are missing here). An outlier can be a rare real case worth studying or an error worth fixing, and you decide which by looking, not by deleting it automatically. A common rule flags values more than 1.5 interquartile ranges beyond the quartiles.
Quick check
You find 12 orders worth ₹0. First move?
A ₹0 order might be a free sample that matters to the business, or a test to leave out.
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Rates, not counts
Predict first
Customers with 3 complaints: 31 of them. Those with none: 3,249. Which group loses a bigger share?
Just show me
The 3-complaint group: 38.7% of them left, against 5% of those with no complaints.
Big groups produce big counts; rates make groups comparable. Divide by each group’s size before comparing cities, months or campaigns, and say how big each group is, because a rate from 31 customers wobbles far more than one from 3,249.
0 complaints (3,249)5%1 complaint (1,420)7.5%2 complaints (295)21.7%3 complaints (31)38.7%Share who left, by complaints in 90 days, with each group’s size
Quick check
Pune had 900 cancellations, Jaipur 300. Which city has the bigger problem?
Cancellations ÷ orders, city by city, before any verdict.
Lesson 1 done.
Next: SQL that answers questions. Most of an analyst’s questions are a JOIN, a GROUP BY and a filter.
In the interview: statistics you use every day.
EasyMean or median: which would you report for order values, and why?
EasyMean, median or mode: how do you find each, and when do you use which?
EasyHow do left-skewed and right-skewed distributions differ?
EasyWhat does a box plot show?
EasyHow do you find the 25th percentile of a column in pandas?
Ask Prism about this lesson
Sources
- The SQL guide’s example shop, its orders, the same in the SQL Lab.
- The ML guide’s churn table, synthetic, 5,000 customers; the figures here computed with pandas.
- Diez, Çetinkaya-Rundel and Barr, “OpenIntro Statistics”, 4th edition, 2019 (CC BY-SA): summaries, spread and outliers.