为庆祝党的二十大的胜利召开,培养担当民族复兴的时代新人,某高校在全校开展“不负韶华,做好社会主义接班人”的宣传活动.为进一步了解学生对党的“二十大”精神的学习情况,学校开展了“二十大”相关知识的竞赛活动,现从参加该活动的学生中随机抽取100人,将他们的竞赛成绩(满分为100分)分为5组:
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%5B%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%5B%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%5B%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%5B%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E%5B%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%5D%3C%2Fmn%3E%3C%2Fmath%3E)
, 得到如图所示的频率分布直方图:
![](http://tikupic.21cnjy.com/2023/04/06/02/ce/02ce3e8ae5dfedd3e93ae04609857032_308x232.png)
参考公式及数据:
, 其中
.
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EK%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
| 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
| 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |