Question

What are the characteristics of a standard normal distribution? Describe some applications for applying a z-score to normalize data. What are the advantages? Disadvantages?

Answer 1

Characteristics of standard normal distribution:

1) Continuous Random Variable.
2) Mound or Bell-shaped curve.
3) The normal curve extends indefinitely in both directions, approaching, but never touching, the horizontal axis as it does so.
4) Unimodal
5) Mean = Median = Mode
6) Symmetrical with respect to the mean
That is, 50% of the area (data) under the curve lies to the left of
the mean and 50% of the area (data) under the curve lies
to the right of the mean.
7) (a) 68% of the area (data) under the curve is within one
standard deviation of the mean
(b) 95% of the area (data) under the curve is within two
standard deviations of the mean
(c) 99.7% of the area (data) under the curve is within three
standard deviations of the mean
8) The total area under the normal curve is equal to 1.

Applications for applying a- score to normalize data:

With a normal distribution of a variable, the mean is the center of the distribution, while the standard deviation shows the level of variability that exists. When you know the value of a variable that is normally distributed, you can calculate the z-score by using the formula:

Z-score:

When you are interested in determining the probability of a specific value occurring, you can use a z-table to look up areas for a calculated z-score to determine the area under the curve of any normal distribution. This can tell you the chance of a value occurring. It should be noted that not all z-score tables are the same.

z-Table

Table for looking up the area starting at z = 0 for a positive z-score

value - mean standard deviation

Advantages to normalization

1) Avoids data modification (INSERT/DELETE/UPDATE) anomalies as each data item lives in One place

2) Greater flexibility in getting the expected data in atomic granular

3) Normalization is conceptually cleaner and easier to maintain and change as your needs change

4) Fewer null values and less opportunity for inconsistency

5) A better handle on database security

6) Increased storage efficiency

Disadvantages of normalization

1) Requires much more CPU, memory, and I/O to process thus normalized data gives reduced database performance

2) Requires more joins to get the desired result. A poorly-written query can bring the database down

3) Maintenance overhead. The higher the level of normalization, the greater the number of tables in the database