what was the average expected volatility rate from 2005 to 2007
Important information:
table_1: assumptions the expected volatility rate of 2007 is 20.80% ( 20.80 % ) ; the expected volatility rate of 2006 is 21.40% ( 21.40 % ) ; the expected volatility rate of 2005 is 22.90% ( 22.90 % ) ;
table_2: assumptions the expected dividend yield of 2007 is 2.92% ( 2.92 % ) ; the expected dividend yield of 2006 is 3.24% ( 3.24 % ) ; the expected dividend yield of 2005 is 3.29% ( 3.29 % ) ;
text_11: the volatility rate is derived by mathematical formula utilizing the weekly high closing stock price data over the expected term .
Reasoning Steps:
Step: add2-1(20.80, 21.40) = 42.2
Step: add2-2(#0, 22.90) = 65.1
Step: add2-3(#1, const_3) = 0.434
Step: divide0-0(#2, const_2) = 21.7%
Program:
add(20.80, 21.40), add(#0, 22.90), add(#1, const_3), divide(#2, const_2)
Program (Nested):
divide(add(add(add(20.80, 21.40), 22.90), const_3), const_2)

Please answer the following financial question based on the context provided. Make sure to give the answer in raw number, not in percentage and without any units. If the question asks for percentage the value should be less than 1
Context:
notes to the audited consolidated financial statements for 2007 , 2006 , and 2005 , total share-based compensation expense ( before tax ) of approximately $ 26 million , $ 29 million , and $ 22 million , respectively , was recognized in selling , general and administrative expense in the consolidated statement of earnings for all share-based awards of which approximately $ 13 million , $ 17 million , and $ 5 million , respectively , related to stock options . sfas no . 123 ( r ) requires that compensation expense is recognized over the substantive vesting period , which may be a shorter time period than the stated vesting period for retirement-eligible employees . for 2007 and 2006 , approximately $ 3 million and $ 8 million , respectively , of stock option compensation expense were recognized due to retirement eligibility preceding the requisite vesting period . stock option awards option awards are granted on an annual basis to non-employee directors and to employees who meet certain eligibility requirements . option awards have an exercise price equal to the closing price of the company's stock on the date of grant . the term life of options is ten years with vesting periods that vary up to three years . vesting usually occurs ratably over the vesting period or at the end of the vesting period . the company utilizes the black scholes merton ( "bsm" ) option valuation model which relies on certain assumptions to estimate an option's fair value . the weighted average assumptions used in the determination of fair value for stock options awarded in 2007 , 2006 , and 2005 are provided in the table below: .
Table
assumptions                     | 2007               | 2006               | 2005              
expected volatility rate        | 20.80% ( 20.80 % ) | 21.40% ( 21.40 % ) | 22.90% ( 22.90 % )
expected dividend yield         | 2.92% ( 2.92 % )   | 3.24% ( 3.24 % )   | 3.29% ( 3.29 % )  
average risk-free interest rate | 4.24% ( 4.24 % )   | 4.62% ( 4.62 % )   | 4.48% ( 4.48 % )  
expected forfeiture rate        | 0.75% ( 0.75 % )   | 0.75% ( 0.75 % )   | actual            
expected term years             | 4.40               | 4.40               | 5.00              
the volatility rate of grants is derived from historical company common stock price volatility over the same time period as the expected term of each stock option award . the volatility rate is derived by mathematical formula utilizing the weekly high closing stock price data over the expected term . the expected dividend yield is calculated using the expected company annual dividend amount over the expected term divided by the fair market value of the company's common stock . the average risk-free interest rate is derived from united states department of treasury published interest rates of daily yield curves for the same time period as the expected term . sfas no . 123 ( r ) specifies only share-based awards expected to vest be included in share-based compensation expense . estimated forfeiture rates are determined using historical forfeiture experience for each type of award and are excluded from the quantity of awards included in share-based compensation expense . the weighted average expected term reflects the analysis of historical share-based award transactions and includes option swap and reload grants which may have much shorter remaining expected terms than new option grants. .
Question: 
what was the average expected volatility rate from 2005 to 2007
Important information:
table_1: assumptions the expected volatility rate of 2007 is 20.80% ( 20.80 % ) ; the expected volatility rate of 2006 is 21.40% ( 21.40 % ) ; the expected volatility rate of 2005 is 22.90% ( 22.90 % ) ;
table_2: assumptions the expected dividend yield of 2007 is 2.92% ( 2.92 % ) ; the expected dividend yield of 2006 is 3.24% ( 3.24 % ) ; the expected dividend yield of 2005 is 3.29% ( 3.29 % ) ;
text_11: the volatility rate is derived by mathematical formula utilizing the weekly high closing stock price data over the expected term .
Reasoning Steps:
Step: add2-1(20.80, 21.40) = 42.2
Step: add2-2(#0, 22.90) = 65.1
Step: add2-3(#1, const_3) = 0.434
Step: divide0-0(#2, const_2) = 21.7%
Program:
add(20.80, 21.40), add(#0, 22.90), add(#1, const_3), divide(#2, const_2)
Program (Nested):
divide(add(add(add(20.80, 21.40), 22.90), const_3), const_2)
