Statistics for Decision- Making in Business - Maricopa Community ...

2.2 to 2.3
2.3 to 2.4
2.4 to 2.5
2.5 to 2.6
2.6 to 2.7
2.7 to 2.8
2.8 to 2.9
2.9 to 3
3 to 3.1
3.1 to 3.2
3.2 to 3.3
3.3 to 3.4
3.4 to 3.5
3.5 to 3.6
3.6 to 3.7
3.7 to 3.8
3.8 to 3.9
3.9 to 4
4 to 4.1
4.1 to 4.2
4.2 to 4.3
4.3 to 4.4
4.4 to 4.5
4.5 to 4.6
4.6 to 4.7
4.7>
120
Sampling Distribution of x-bar
100
80
60
40
20
0
The distribution looks a bit more normal. Upon closer inspection, we also see that the variability
of these averages is smaller. That is:
Approximate Range for Means of 10 Tosses: 2.1 to 5.2
Approximate Range for Means of 20 Tosses: 2.5 to 4.6
We notice that increasing the sample size ( ) has decreased the sampling distribution‟s
variability.
In fact, the standard deviation for the distribution of means computed from 10 and 20 tosses is
about 0.52 and 0.38, respectively.
Let‟s do one more experiment. Let‟s say that 1000 individuals each roll a die 30 times, and each
individual computes the mean of his/her rolls. The sampling distribution of means would look
like this (based on simulation):
Statistics for Decision-Making in Business © Milos Podmanik Page 186