中六統計題？？？？？？

[匿名]

2012-04-15 2:11 pm

以下是一群小童的上網時數分佈

每日上網2小時有R人，3小時8人，4小時12人，5小時S人
R和S均為正數

a：求該分佈的四分位數間距的最小可取值及最大可取值。
b：若R=9及該分佈的中位數為3，則S有多少個可取值？試解釋你的答案。

更新1:

唔好意思，可唔可以用中文

回答 (1)

用戶10012

2012-04-15 3:27 pm

✔ 最佳答案

a)
Case (I) Both R and S are large (say R = S = 800)
Total = 1620, 1stQ = 1620/4 = 405. So IQR = 5 - 2 = 3 which is the largest possible value of IQR.
Case (II) R small ( = 1) and S large ( = 999)
Total = 1020, 1stQ = 1020/4 = 255. So IQR = 5 - 5 = 0 which is the smallest possible value of IQR.
Case (III) R large ( = 999) and S small ( = 1)
Total = 1020, 1stQ = 1020/4 = 255. So IQR = 2 - 2 = 0.
b)
If median = 3, the maximum total no. of children < (9 + 8) x 2 < 34
so S < (34 - 9 - 8 - 12) < 5. That is max. S = 4.
So S can be 1,2,3 or 4.

2012-04-15 07:29:34 補充：
Note : Zero is not positive nor negative.

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