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Comparing Data Sets

A fair comparison of two data sets always uses an average AND a measure of spread together.

Average Alone Is Not Enough

Two data sets can share the exact same average, and still be very different. Always compare BOTH an average (mean or median) AND a measure of spread (range or IQR) to get the full picture.

Example 1 — same mean, different spread

Class A's test scores have a mean of 65 and a range of 10 . Class B's test scores have a mean of 65 and a range of 40 . Compare them. 1 Both classes performed the same on average (mean = 65) 2 Class A's range (10) is much smaller than Class B's (40) Conclusion: Class A's results were far more consistent. Class B had much more variation — some students scored very differently from others.

Example 2 — using median and IQR

Two delivery companies both have a median delivery time of 50 minutes. Company X has an IQR of 5 minutes. Company Y has an IQR of 25 minutes. Compare them. 1 Both companies have the same typical (median) delivery time 2 Company X's smaller IQR means its delivery times are far more consistent Conclusion: Company X is more reliable — a customer can trust the delivery time will be close to 50 minutes. Company Y's times vary much more widely.

Practice

Two machines produce parts with the same mean length. Machine 1 has a range of 0.2 mm. Machine 2 has a range of 3 mm. Which machine is more consistent?

Average Alone Is Not Enough

Two data sets can share the exact same average, and still be very different. Always compare BOTH an average (mean or median) AND a measure of spread (range or IQR) to get the full picture.

Example 1 — same mean, different spread

Class A's test scores have a mean of 65 and a range of 10 . Class B's test scores have a mean of 65 and a range of 40 . Compare them. 1 Both classes performed the same on average (mean = 65) 2 Class A's range (10) is much smaller than Class B's (40) Conclusion: Class A's results were far more consistent. Class B had much more variation — some students scored very differently from others.

Example 2 — using median and IQR

Two delivery companies both have a median delivery time of 50 minutes. Company X has an IQR of 5 minutes. Company Y has an IQR of 25 minutes. Compare them. 1 Both companies have the same typical (median) delivery time 2 Company X's smaller IQR means its delivery times are far more consistent Conclusion: Company X is more reliable — a customer can trust the delivery time will be close to 50 minutes. Company Y's times vary much more widely.

Practice

Two machines produce parts with the same mean length. Machine 1 has a range of 0.2 mm. Machine 2 has a range of 3 mm. Which machine is more consistent?