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Infinite · 2020年02月13日

问一道题: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).

没有看明白为什么25%是5/20,为什么是2和3的观察值,75%为什么又找的是4和5的观察值?

1 个答案

orange品职答疑助手 · 2020年02月13日

25%是介于20%-40%中间的。间距20%,而25%比20%仅高出5%,靠进20%更近,所以应该20%的分位数所占的权重应该是(20%-5%)/20% = 3/4。因此,25%应该由15/20*20%的分位数 + 5/20*40%的分位数得到。

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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

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2024-02-03 15:28 2 · 回答

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NO.PZ2020010304000036 求分位点分母为什么是n-1?

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NO.PZ2020010304000036 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!

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