What does "weighted average''(加權平均數) mean??

It is not an average at all.

Why the atomic mass is seldom a whole number?

Why potassium is more reactive than sodium??

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What does "weighted average''(加權平均數) mean?? It is not an average at all.

The weighted average is a form of average. In case that some data points contribute more than others, the data points are said to be having different weights. The weighted average is the average which is calculated based on the data points with their weights.

For example, the relative abundance of 35Cl and 37Cl are 75% and 25% respectively. Their relative isotopic masses are 35 and 37 respectively, which contribute with different weights 75% : 25%. In calculation of "average" of the isotopic masses (i.e. the relative atomic mass), it is undesirable to calculate the average of 35 and 37 (i.e. 36). Instead, the weighted average should be calculated.

Hence, the relative atomic mass of Cl

= Weighted average of all the relative isotopic mass

= 35x75% + 37x25%

= 35.5

Why the atomic mass is seldom a whole number?

The atomic mass (the short form of relative atomic mass) of an element is the weighted average of all isotopic masses of all isotopes of the element. Since the weights (relative abundance) are not whole numbers, thus the weighted average is usually not a whole number.

Why potassium is more reactive than sodium??

Both potassium and sodium are metals, which lose the outermost shell electrons in reaction. Since potassium atom has more electronic shells are thus a larger size than sodium atom, thus the electron potassium atom loses the outermost shell electron more readily. Therefore, potassium is more reactive than sodium.

2009-08-25 20:06:44 補充：

加權的意思是計算其比重。例如有兩個數據 5 (出現兩次) 和 8。

加權是指要考慮 5 出現了兩次，所以加權平均

= (5x2 + 8)/(2 + 1) = 6

若不加權的話，平均

= (5 + 8)/2 = 6.5

2009-08-25 20:12:17 補充：

所謂加權平均就是要計算每個數據的比重。例如有兩個數據： 5 (出現兩次) 和 8。

計算平均是加權，就要考慮到 5 出現到兩次。加權平均

= (5x2 + 8)/2

= 6

若果加權，就只計算 5 和 8 的平均，平均

= (5 + 8)/2

= 6.5

2009-08-25 20:15:03 補充：

所謂加權平均就是要計算每個數據的比重。例如有兩個數據： 5 (出現兩次) 和 8。

計算平均是加權，就要考慮到 5 出現到兩次。加權平均

= (5x2 + 8)/2

= 6

若果加權，就只計算 5 和 8 的平均，平均

= (5 + 8)/2

= 6.5

2009-08-25 20:15:30 補充：

所謂加權平均就是要計算每個數據的比重。例如有兩個數據： 5 (出現兩次) 和 8。

計算平均是加權，就要考慮到 5 出現到兩次。加權平均

= (5x2 + 8)/2

= 6

若果不加權，就只計算 5 和 8 的平均，平均

= (5 + 8)/2

= 6.5

2009-08-25 20:16:06 補充：

所謂加權平均就是要計算每個數據的比重。例如有兩個數據： 5 (出現兩次) 和 8。

計算平均是加權，就要考慮到 5 出現到兩次。加權平均

= (5x2 + 8)/2

= 6

若果不加權，就只計算 5 和 8 的平均，平均

= (5 + 8)/2

= 6.5