ByColin Sundwick

SAT Math ScoresVariable N N* Mean SE Mean StDev Minimum Q1 Median Q3Math 390 56 610.44 3.65 72.14 400.00 560.00 610.00 660.00

μ= 610.44σ= 72.14

The shape is fairly normal.

Random Small SamplesNext, I randomly

sampled 10 rows of math SAT scores 20 times and recorded the mean of each small sample.

57 25858 55859 560 238861 5862 126663 17646566 2

Stem-and-Leaf PlotCenter- 608Spread- 23.32Shape- fairly normal

except for one high value.

57 25858 55859 560 238861 5862 126663 17646566 2

Random LARGE SamplesNext, I did the same

thing, except with 40 rows instead of 10.

58 859 459 5960 060 789961 013461 56862 00462 5

Stem-and-Lead PlotCenter- 610.5Spread- 10.31Shape- pretty

normal

58 859 459 5960 060 789961 013461 56862 00462 5

How do they compare? Samples of 10 Samples of 40Center- 608Spread- 90Shape- fairly normal

with one apparent outlier, even though the 1.5 x IQR rule doesn’t classify it as one.

Center- 609.5Spread- 37Shape- normal

Boxplots

Wages Earned Variable N N* Mean SE Mean StDev Minimum Q1 Median

Q3 Earned 446 0 3.776 0.308 6.503 0.000 1.000 2.000

4.000

μ = 3.776σ= 6.503

The graph is clearly skewed right

Random Small SamplesNext, I randomly sampled

10 rows of wages earned 20 times and recorded the mean of each small sample.

1 672 013442 773 043 7994 34 65 35 666 577 8

Stem-and-Leaf PlotCenter- 3.2Spread- 1.68Shape- skewed right

1 672 013442 773 043 7994 34 65 35 666 577 8

Random Large SamplesNext, I did the same

thing, except with 40 rows instead of 10.

2 12 5663 0012233 57784 002234 8

Stem-and-Leaf PlotCenter- 3.4Spread- .709Shape- normal

2 12 5663 0012233 57784 002234 8

How do they compare?Samples of 10 Samples of 40Center- 3.2Spread- 1.68Shape- skewed right

Center- 3.4Spread- .709Shape- normal

Boxplots

THE END