解题方法
1 . 树人中学男女学生比例约为
,某数学兴趣社团为了解该校学生课外体育锻炼情况(锻炼时间长短(单位:小时),采用样本量比例分配的分层抽样,抽取男生
人,女生
人进行调查.记男生样本为
,
,
,
,样本平均数、方差分别为
、
;女生样本为
,
,
,
,样本平均数、方差分别为
、
;总样本平均数、方差分别为
、
.
(1)证明:
;
(2)该兴趣社团通过分析给出以下两个统计图,假设两个统计图中每个组内的数据均匀分布,根据两图信息分别估计男生样本、女生样本的平均数;
(3)已知男生样本方差
,女生样本方差
,请结合(2)问的结果计算总样本方差
的估计值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4806fb7f95f63e863c287faa51f8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad7f66c97bfce4c00c53d86700c961b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbc29b47b83fdc5368770b7b1acb439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb525270c748eddaaecc4a549cca250e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f6aeb6ba39321159128713fa17ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/f2f3f252-1fa3-4b50-b9dc-aa3f8f88a1a7.png?resizew=489)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23085de75111f933e1232906fd69f36.png)
(2)该兴趣社团通过分析给出以下两个统计图,假设两个统计图中每个组内的数据均匀分布,根据两图信息分别估计男生样本、女生样本的平均数;
(3)已知男生样本方差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9c4a8a890d59851e348a822e7e0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6c9b4cc7bb4d740abbe799f3c22134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
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