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====== Frequency distribution table ======

===== Simple frequency table =====

After grouping the data of the same value, the number of times which each value occurs can be obtained. These times are expressed in the form of a table, by arranging the data (X) in a column by increasing sequence, and then listing the number of times each value occurs(f) in another column , which gives the simplest frequency distribution table.

Each cell of column f in the simple frequency table lists the number of times the value occurs. In order to calculate the number of all the data, we just need to add up all the data in column f, i.e.:

{{ :2.1.1.png?100 |}}

Sometimes we need to calculate the sum of variables. At this point we could add up all the fractions, i.e:

{{ :2.1.2.png?100 |}}

Proportions are the proportions of the whole group with value X. The formula is as follows.

{{ :2.1.3.png?100 |}}

Percentages are the conversions of proportions in decimal form multiplied by 100.

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===== Grouped frequency table =====

当样本可取的数据的数值比较多时，我们就需要对数值进行分组。进行分组数据统计，关键的一点就是划分数据区间，也就是确定每组的取值范围。每组中包含的数据值的最大值与最小值的差距我们称为组距，一般来说，81-90的数据组，我们认为80.5为数据值的最小值，而90.5为数据的最大值。全部数据的最大值与最小值的差距叫做全距。而当组数确定之后，我们可以大概确定组距，三者的关系为：

{{ :2.1.4.png?100 |}}

当然，组距一般取较为简单的数字，如10或者5的倍数，而且每组的起点也应该尽量简单。