Home Mutual Funds The Normal Distribution Table Definition

# The Normal Distribution Table Definition

## What Is the Normal Distribution?

The normal distribution formula is based on two simple parameters—mean and standard deviation—that quantify the characteristics of a given dataset.

While the mean indicates the “central” or average value of the entire dataset, the standard deviation indicates the “spread” or variation of data points around that mean value.

### Key Takeaways

• The normal distribution formula is based on two simple parameters—mean and standard deviation—that quantify the characteristics of a given dataset.
• To facilitate a uniform standard method for easy calculations and applicability to real-world problems, the standard conversion to Z-values was introduced, which form the part of the Normal Distribution Table.
• Properties of a normal distribution include: the normal curve is symmetrical about the mean; the mean is at the middle and divides the area into halves; the total area under the curve is equal to 1 for mean=0 and stdev=1; and the distribution is completely described by its mean and stddev.
• Normal distribution tables are used in securities trading to help identify uptrends or downtrends, support or resistance levels, and other technical indicators.

## Normal Distribution Example

Consider the following 2 datasets:

1. Dataset 1 = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}
2. Dataset 2 = {6, 8, 10, 12, 14, 14, 12, 10, 8, 6}

For Dataset1, mean = 10 and standard deviation (stddev) = 0

For Dataset2, mean = 10 and standard deviation (stddev) = 2.83

Let’s plot these values for DataSet1:

Similarly for DataSet2:

The red horizontal line in both the above graphs indicates the “mean” or average value of each dataset (10 in both cases). The pink arrows in the second graph indicate the spread or variation of data values from the mean value. This is represented by standard deviation value of 2.83 in case of DataSet2. Since DataSet1 has all values same (as 10 each) and no variations, the stddev value is zero, and hence no pink arrows are applicable.

The stddev value has a few significant and useful characteristics which are extremely helpful in data analysis. For a normal distribution, the data values are symmetrically distributed on either side of the mean. For any normally distributed dataset, plotting graph with stddev on horizontal axis, and number of data values on vertical axis, the following graph is obtained.

## Properties of a Normal Distribution

1. The normal curve is symmetrical about the mean;
2. The mean is at the middle and divides the area into two halves;
3. The total area under the curve is equal to 1 for mean=0 and stdev=1;
4. The distribution is completely described by its mean and stddev

As can be seen from the above graph, stddev represents the following:

• 68.3% of data values are within 1 standard deviation of the mean (-1 to +1)
• 95.4% of data values are within 2 standard deviations of the mean (-2 to +2)
• 99.7% of data values are within 3 standard deviations of the mean (-3 to +3)

The area under the bell-shaped curve, when measured, indicates the desired probability of a given range:

• less than X: e.g. probability of data values being less than 70
• greater than X: e.g. probability of data values being greater than 95
• between X1 and X2: e.g. probability of data values between 65 and 85

where X is a value of interest (examples below).

Plotting and calculating the area is not always convenient, as different datasets will have different mean and stddev values. To facilitate a uniform standard method for easy calculations and applicability to real-world problems, the standard conversion to Z-values was introduced, which form the part of the Normal Distribution Table.

Z = (X – mean)/stddev, where X is the random variable.

Basically, this conversion forces the mean and stddev to be standardized to 0 and 1 respectively, which enables a standard defined set of Z-values (from the Normal Distribution Table) to be used for easy calculations. A snap-shot of standard z-value table containing probability values is as follows: