Milk-carton example
Section of Statistical inference, part of Statistical inference
Milk-carton example
| Type | Section |
| Taught in | Statistical inference |
| Part | Statistical inference |
A machine fills cartons that must legally hold at least 1 litre. Filling always varies, so the machine is set to a target of 1.10 litres. Were it set to exactly 1 litre, about half the cartons would be under-filled. To check whether the machine is still on target, 10 cartons are chosen at random and measured, in litres:
| Cartons 1–5 | 1.035 | 1.019 | 1.068 | 1.084 | 1.077 |
|---|---|---|---|---|---|
| Cartons 6–10 | 0.998 | 1.041 | 1.037 | 1.051 | 1.102 |
The sample mean is \overline x=1.0512, the sample median is 1.0460, and the bias-corrected sample standard deviation is s=0.0317. The range is 1.102-0.998=0.104. Sorted, the ten values are 0.998, 1.019, 1.035, 1.037, 1.041, 1.051, 1.068, 1.077, 1.084 and 1.102, so the lower quartile, the median of the five values below the median, is 1.035, and the upper quartile is 1.077.
Do these numbers show that the machine is off target? Every one of them would change if another 10 cartons were measured. The question cannot be answered from the numbers alone. It needs a model for how the numbers came about.
Used in
- Taught in Statistical inference
- Also used in Estimation
- All 4 questions on Statistical inference
See also
Random sample · Statistic · Moments of the sample mean and variance · Chi-squared distribution · Student t distribution · F distribution · Normal sample theorem · Degrees of freedom