Choose a method
Identify the sample size and measurement units. Recover a missing total from a mean; sort the observations before locating the median.
Avoid this trap
Changing every observation by the same amount changes the center but leaves the spread unchanged. A model prediction is not an observed measurement.
Check and transfer
Distinguish describing this sample from generalizing to a population. A stated random sample supports a different inference than a convenience sample.
Worked example with a numerical check
The mean of four measurements is 10. Three measurements are 4, 8 and 12. What is the fourth? Multiply the mean by four to recover the total. Subtract the sum of the known measurements. The requested value is 16.
Contrast and diagnose
The dot plot shows all five observations. What is the median? Dot plot: one observation at each of 4, 6, 8, 12, 14. Sort the five observations from smallest to largest. Select the third observation, leaving two on either side. The requested value is 8. An incorrect approach: Use the midpoint of extreme values.
Transfer practice
A data set has minimum 4 and maximum 16. Each value is increased by 7. What is the new range? Try first. Check: 12. The minimum and maximum each increase by the same amount. Their difference is unchanged by this common shift.
The mean of four measurements is 10. Three measurements are 4, 8 and 12. What is the fourth?
- Multiply the mean by four to recover the total.
- Subtract the sum of the known measurements.
- The requested value is 16.
Compare the other answer choices
Copy the first known measurement instead of solving for the missing observation.
Multiply the mean by only the three known observations.
Use the mean as the missing observation.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Math specifications