QNT 275 Week 2 participation The Z-score

Select a specific year from the Wisconsin Water Table, and find the Z-score for the associated data point (water discharge)

Year                                      Peak Discharge

1957                                                                                                  1,120

1958                                                                                                  2,380

1959                                                                                                  886

1960                                                                                                  1,420

1961                                                                                                  1,480

1962                                                                                                  1,200

1963                                                                                                  657

1964                                                                                                  1,280

1965                                                                                                  1,640

1966                                                                                                  1,280

1967                                                                                                  1,740

1968                                                                                                  1,380

(source: U.S. Department of the Interior, Geological Survey, Water Resources Divisions, Estimating Magnitude and Frequency of Floods in Wisconsin, 1971. p. 77. I19.2:W75)

The Z-Score

Team

It is not until we augment the Standard Deviation with a Z-score the standard deviation makes sense, such as the case with the Wisconsin Water Table. A Z-Score is a statistical formula that tells us where a specific data point falls on the bell curve in relationship to the mean/mode/median of the bell curve which is the exact middle of the curve. The Z-score tells us how many standard deviations a specific data point falls above OR below the middle of the curve (+ or –

Let’s look at the Wisconsin Water Table to explain this process:

In order to get the Z-score for the year 1960. All you need to do is  find the Standard deviation and the mean for the Wisconsin Water table (which we have just done in Week 1).

Xbar or μ = 1,371.91

s or σ = 436

Your observation is X which for 1960 is 1,420. Insert in the following formula:

z=   X – μ

σ

.11 =        1,420 – 1,371.91

436

The Z-score falls .11 standard deviations ABOVE the mean. Look how close the amount of water discharge was for 1960 as compared to the mean of the water discharge (1,371.91). It is so close it practically kisses the mean.

This Z-score tells us that the water output for the year 1960 was just slightly greater (not by much) than the average discharge of all the years combined. Does this make sense?