Yesterday, I concluded my post Calculating Normalized P/E Ratios with this graph of the percentage difference between the Dow's actual earnings and its 15-year normalized earnings for each year from 1935-2005:

*click charts to enlarge*

I also wrote:

The difference between actual earnings and normalized (or "expected") earnings is one of the most fascinating statistics in this little study.

To better understand this statistic we need to look at its distribution over the 71 years in this study.

First, let's look at a graph of the difference between the Dow's actual earnings and its 15-year normalized earnings for each of the last seventy-one years. But, this time, instead of presenting the data in chronological order, I will simply plot the data in ascending order by difference between actual and normalized earnings:

Based on this graph, you would probably guess that the Dow's actual earnings have been higher than its normalized earnings about half the time and lower than its normalized earnings about half the time.

That's quite right. From 1935-2005, the difference between the Dow's actual earnings and its normalized earnings was positive in 36 years and negative in 35 years.

**Distribution of the Data**

From 1935-2005, the percentage difference between the Dow's actual earnings and its 15-year normalized earnings ranged from (62.12%) to 65.14%. The average (mean) difference between actual and normalized earnings was 0.44%. The median difference was 0.09%.

According to the "empirical rule", in a normal (bell-shaped) distribution, about 68% of the values will be within one standard deviation of the mean, about 95% of the values will be within two standard deviations of the mean, and about 99.7% of the values will be within 3 standard deviations of the mean.

In our little study, 49 of 71 values (69.01%) are within one standard deviation of the mean, 67 of 71 values (94.37%) are within two standard deviations of the mean, and 71 of 71 values (100%) are within three standard deviations of the mean. No value is more than 2.5 standard deviations from the mean. In fact, the greatest distance between a value and the mean is 2.26 standard deviations.

Of the 49 values within one standard deviation, 24 are positive and 25 are negative. Of the 67 values within two standard deviations, 34 are positive and 33 are negative.

**Frequency of Various Differences**

I can quickly give you some sense of how common large and small differences between the Dow's actual earnings and its 15-year normalized earnings were from 1935-2005.

Remember, negative numbers mean actual earnings fell below normalized earnings; positive numbers mean actual earnings exceeded normalized earnings.

(71.24%) – (56.90%): 2 of 71 years or 2.82% of the time

(56.90%) – (42.57%): 2 of 71 years or 2.82% of the time

(42.57%) – (28.23%): 6 of 71 years or 8.45% of the time

(28.23%) – (13.90%): 13 of 71 years or 18.31% of the time

(13.90%) – 0.44%: 13 of 71 years or 18.31% of the time

0.44% - 14.78%: 15 of 71 years or 21.13% of the time

14.78% - 29.11%: 8 of 71 years or 11.27% of the time

29.11% - 43.45%: 6 of 71 years or 8.45% of the time

43.45% - 57.78%: 4 of 71 years or 5.63% of the time

57.78% - 71.68%: 2 of 71 years or 2.82% of the time

I'll be discussing the difference between the Dow's actual earnings and its normalized earnings quite a bit in the weeks ahead. Today, I just wanted to provide a general overview of this statistic and what it has looked like in the past, before we discuss it in detail. In future posts, I'll explore its importance for investors.

**Related Reading**

Calculating Normalized P/E Ratios

On Normalized P/E Effects Over Time

A Second Look At Normalized P/E Ratios and the Election Cycle