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Luhunlu · 2022年02月18日

老师,请问以后这种题都是这样做吗?

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).

做题思路都是默认第一个数的概率是0%,然后其余的数平分100%的概率,并按照从小到大和累计概率来排序,是这样吗?


假如这道题是11个数,那么升序排列后概率依次为0%、10%······100%,

(假如还是这些数)四分之一分位点就是:q25%=0.27*50%+0.28*50%=0.275;

或者用线性差值法来做:(x-0.27)/(0.28-0.27)=(25%-20%)/(30%-20%)


辛苦老师解答!

1 个答案

李坏_品职助教 · 2022年02月18日

嗨,从没放弃的小努力你好:


对的,就是这样。先从0到100%平分概率,从小到大排序,然后根据25%与相邻两个概率的差额,来决定差值的权重。如果是11个数,那么25%分位点就在20%和30%之间,是这两个临界点各占0.5。

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