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stephanie_liu · 2021年04月20日

25%的位置为什么需要在rank20%对应的0.27出发到rank40%的0.28之间取，而不是1和2的位置取呢，为什么计算公式这样算，而不是各乘以50%

  1. FRM I
  2. Quantitative

NO.PZ2020010304000036

问题如下：

For the following data:

a. What is the median?

b. What is the IQR?

选项：

解释：

a. The first step is to rank order the observations.

From here, we anchor the first observation at 0% and the last at 100%, equally spacing the in-between val-ues. The divisions here will be 100/n-1 = 20%:

The median (50%) lies exactly half way between the third and fourth ranked observations. Therefore:

Median=(0.28+0.38)/2=0.33

b. This requires calculating the 25% and 75% levels.

The 25% level is 5/20 = 25% of the way between ranked observations 2 and 3. Therefore: q25% = 0.75 * 0.27 + 0.25 * 0.28 = 0.2725

Similarly, the 75% level is 75% of the way between observations 4 and 5: q75% = 0.25 * 0.38 + 0.75 * 0.43 = 0.4175

Thus, IQR = (0.2725, 0.4175).


25%的位置为什么需要在rank20%对应的0.27出发到rank40%的0.28之间取，而不是1和2的位置取呢，为什么计算公式这样算，而不是各乘以50%


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1 个答案

小刘_品职助教 · 2021年04月20日

同学你好，

第一个问题，因为一共有6个观察数据，按照从0到100%这样排列，所以第1个数据是0%，第二个数据是20%，第三个数据是40%……第6个数据是100%分位点。

所以25%的分位数是在第2个位置和第3个位置之间进行选择。

第二个问题，因为这是按照线性插值法计算的逻辑其实是

（25-20）/(x-0.27)=(40-20)/(0.28-0.27) 计算可得，x=0.2725

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NO.PZ2020010304000036问题如下For the following ta:Whis the mean? Whis the IQR?The first step is to rank orr the observations.From here, we anchor the first observation 0% anthe last 100%, equally spacing the in-between val-ues. The visions here will 100/n-1 = 20%:The me(50%) lies exactly half wbetween the thiranfourth rankeobservations. Therefore:Mean=(0.28+0.38)/2=0.33 This requires calculating the 25% an75% levels.The 25% level is 5/20 = 25% of the wbetween rankeobservations 2 an3. Therefore: q25% = 0.75 * 0.27 + 0.25 * 0.28 = 0.2725Similarly, the 75% level is 75% of the wbetween observations 4 an5: q75% = 0.25 * 0.38 + 0.75 * 0.43 = 0.4175Thus, IQR = (0.2725, 0.4175). 老师，这种方式也叫插分吗？

2024-05-13 16:04 1 · 回答

NO.PZ2020010304000036 问题如下 For the following ta:Whis the mean? Whis the IQR? The first step is to rank orr the observations.From here, we anchor the first observation 0% anthe last 100%, equally spacing the in-between val-ues. The visions here will 100/n-1 = 20%:The me(50%) lies exactly half wbetween the thiranfourth rankeobservations. Therefore:Mean=(0.28+0.38)/2=0.33 This requires calculating the 25% an75% levels.The 25% level is 5/20 = 25% of the wbetween rankeobservations 2 an3. Therefore: q25% = 0.75 * 0.27 + 0.25 * 0.28 = 0.2725Similarly, the 75% level is 75% of the wbetween observations 4 an5: q75% = 0.25 * 0.38 + 0.75 * 0.43 = 0.4175Thus, IQR = (0.2725, 0.4175). 应该怎么求？没看懂解析。

2024-02-03 15:28 2 · 回答

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2022-06-23 13:57 1 · 回答

NO.PZ2020010304000036 求分位点分母为什么是n-1？

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2022-02-18 18:05 1 · 回答