MediumStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Spread of DataNumericalConceptual
Two machines fill bottles with juice. A quality check takes five bottles from each, in millilitres…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two machines fill bottles with juice. A quality check takes five bottles from each, in millilitres. Machine A: . Machine B: . These are made-up data. Treat each set of five as a sample. Find the mean and the sample standard deviation of each machine, to two decimal places. Which machine is more consistent?
Need a reminder? The key ideaShow
Deviations from the mean add up to zero. The MAD averages their sizes; the variance averages their squares. Population (whole group): divide by . Sample: divide by .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Means. Both totals are 2500 mL, so both means are 500 mL.
Step 2. Machine A. Deviations ; squares add up to 10. mL.
Step 3. Machine B. Deviations ; squares add up to 68. mL.
Answer: both means are 500 mL; mL for A and mL for B. Machine A is more consistent.
What if? The same mean hides very different machines. A customer of machine B could get 495 mL; a customer of machine A never gets less than 498 mL.
Discussion (0)
Log in to join the discussion.
Loading…