Vol. 11, No. 10
October 2009
PQ Systems
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Quality Quiz from Professor Cleary

Predicting behavior of averages can be as fascinating as predicting the behavior of animals. Hartford Simsack, the intrepid quality manager for Greer Grate & Gate, sometimes thought of himself as a visitor to the zoo, watching his averages and trying to anticipate what to him was always a complete surprise in the behavior of data. “I never know if this is going to turn out to be a normal distribution or not,” he told his mentor, Dr. Stan Deviation.

Dr. Deviation cleared his throat, then reminded Simsack yet again that one of the keys to predicting the shape of the averages lies in sample size. Regardless of the distribution shape of the parent population, the distribution of sample means from that population will tend to follow a normal distribution as the sample size increases. You will remember that in last month’s quiz, Dr. Deviation demonstrated a simulation model with 1,000 samples of the size 1 and 2 from two populations to demonstrate the shape of the distributions from both. Unfortunately, Simsack does not recall either the column, or his mentor’s lecture about this point.

The charts below demonstrate how the shape of the sample means changed for sample size of 1 and 2 for two very different shaped populations.

For sample size of 1:

Population       Distribution of sample means (n=1)

For sample size of two:

Population       Distribution of sample means (n=2)

Hartford Simsack could never quite get his mind around this concept. Unfortunately for him, however, his boss, Rock DeBote, did, and asked him often for an explanation. DeBote not only wanted an answer, but he wanted to understand the concept well enough that he could derive his own understanding. After his conversation with Dr. Deviation, he was quick to respond to nearly every question about distributions was that “it all depends on sample size.” DeBote was not content with this superficial answer, pressing Simsack for the statistical concept responsible for this outcome.

“It’s the central limit theorem,” Simsack responded smugly. This was a term with which he was familiar, and it was what came immediately to his lips. Is he correct?

a) Yes

b) No

 

Click here for a more complete video explanation

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