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LilyRosemary · 2022年03月24日

cumulative relative frequency是啥

NO.PZ2021061603000009

问题如下:

An investment fund has the return frequency distribution shown in the following exhibit:


Which of the following statements is correct?

选项:

A.The relative frequency of the bin "-1.0 to +2.0" is 20%

B.The relative frequency of the bin "+2.0 to +5.0" is 23%

C.The cumulative relative frequency of the bin "+5.0 to +8.0" is 91.7%.

解释:

A is correct. The relative frequency is the absolute frequency of each bin divided by the total number of observations. Here, the relative frequency is calculated as: (12/60) x 100 = 20%. B is incorrect because the relative frequency of this bin is (23/60) x 100 = 38.33%. C is incorrect because the cumulative relative frequency of the last bin must equal 100%.

为啥cumulative relative frequency等于100%

1 个答案

星星_品职助教 · 2022年03月24日

同学你好,

只有“the last bin”所对应的cumulative relative frequency为100%.

需要区分以下几个概念:

absolute frequency相当于每一行的绝对情况,例如第二行的absolute frequency=7.

cumulative指的是累积,第二行的cumulative absolute frequency就等于第一行的3再累加上第二行的7,结果为10.

relative frequency指的是相对频率,第二行的relative frequency=7 / (3+7+10+12+23+5).而此时第二行的cumulative relative frequency为(3+7)/(3+7+10+12+23+5)

以此类推,等到在last bin时,相当于已经累积了所有的数字。在本题中就相当于 (3+7+10+12+23+5)/(3+7+10+12+23+5),必然是100%