What does a typical value hide?

A training column contains eight synthetic measurements: 2, 3, 3, 4, 4, 5, 5, 8. You need one number to describe a typical record. Would your answer change if the last measurement were 80?

You need addition, division, and ordering numbers. Open Explore dataset ↗ to inspect the reference records in a separate tab. These are deliberately small teaching data, not a sample from a real population.

Record a reference

Keep Last record value at 8. Before recording the run, predict where the mean and median will fall. Write your reason and select Record run.

Now change only the last value to 80. Keep the other seven records and the record count fixed. Predict which summary will move more. Record the second run and compare the numbers with run 1. Use the plot and calculated records to identify exactly what changed.

Eight synthetic measurements. The first seven values stay 2, 3, 3, 4, 4, 5, 5. Change only the eighth value; the number of records stays fixed.

Last record value048164080160

Prediction and reason

Record runReference settings

0/16 runs. Each run keeps its own inputs and results. Work stays in this tab across reloads; download a report before closing it.

Write a prediction to record your reference.

Observations: cite runs and valuesExplanation: what accounts for the change?Your next test, prediction, and a result that would challenge it

Download report

Write an explanation using the two runs before opening the reasoning.

Why one record moves the mean

The reference sum is 34, so its mean is $34/8=4.25$. Replacing 8 with 80 adds 72 to the sum and moves the mean to $106/8=13.25$. Most records are still between 2 and 5.

For eight sorted values, the median averages positions four and five. Both remain 4, so the median stays 4. The mean responds to the size of every value; the median depends on the middle positions. A median can change too—its stability in this comparison is not a universal guarantee.

Choose the summary for the question

The mean is $\bar x=\sum x_i/n$. Multiplying it by the record count recovers the total. The median locates the middle of the ordered records. A large measurement may be a valid rare event, a unit mismatch, or a collection error; the summaries cannot decide which.

For data preparation, inspect the records behind a surprising summary before changing them. A numeric customer identifier has an arithmetic mean, but that number usually has no useful measurement interpretation. NIST describes these distinct measures of location.

Design a comparison

Choose a last value we have not tested. Predict the new mean using the change in the sum, then test it. Choose a second value on the other side of the middle and predict whether the median changes. Keep the first seven records fixed and select the appropriate Comparison baseline.

For transfer, imagine adding 10 to every record instead. What happens to both summaries? Write your reasoning and download your report.

Check your transfer argument

Both increase by 10. The sum increases by $8\times10$, and adding the same number preserves order and shifts both middle values by 10. This is a different intervention from changing only one record.

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