تمثيل البيانات، التوزيعات الطبيعية والارتباط
ACT الموضوع 16 5:31 سرد باللغة الإنجليزية · ترجمة مدمجة بالإنجليزية + الصينية
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النص الصوتي
A frequency counts repeated observations.
频率表示重复观测的次数。
Values one, three, seven with frequencies two, one, one represent four observations: one, one, three, seven.
数值1、3、7对应的频数分别为2、1、1，代表四次观测：1、1、3、7。
X bar equals the sum of f times x divided by the sum of f, which is two times one plus one times three plus one times seven, all over four, equals three.
x平均等于f乘x的总和除以f的总和，即两乘一加一乘三加一乘七，整体除以四，等于三。
The median is one plus three, all over two, equals two; it need not equal the mean.
中位数为一加三除以二，等于二；它不必等于均值。
Each task gives its own data.
每个任务都有各自的数据。
Do not copy the worked example’s numbers.
请勿照搬例题中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
Under the stated normal model, about 68 percent lie between 74 and 86, and 95 percent between 68 and 92.
在题目给出的正态模型下，大约百分之六十八的数据落在七十四到八十六之间，百分之九十五落在六十八到九十二之间。
The transformed mean is 2 times 80 plus 5, which is 165, and the standard deviation is 2 times 6, which is 12.
变换后的平均数是二乘八十加五，等于一百六十五，标准差是二乘六，等于十二。
These are model proportions, not guarantees for a finite sample.
这些是模型给出的比例，而不是对有限样本的保证。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
The prediction is 4 times 5 plus 3, which is 23.
预测值是四乘五加三，等于二十三。
The residual is observed minus predicted, 20 minus 23, which is negative 3.
残差等于观测值减预测值，二十减二十三，等于负三。
A positive slope gives association under the fit; confounding or selection can explain it without a direct cause.
正斜率说明在这个拟合下存在关联；混杂因素或选择偏差也能解释这种关联，而不一定存在直接的因果关系。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
The median, Q 2, is 6 plus 9 over 2, which is 7.5.
中位数 Q2 等于六加九除以二，即七点五。
The lower half, 2, 4, 4, 6, has Q 1 equal to 4; the upper half, 9, 11, 12, 16, has Q 3 equal to 11.5.
下半部分二、四、四、六的 Q1 是四；上半部分九、十一、十二、十六的 Q3 是十一点五。
The five-number summary is 2, 4, 7.5, 11.5, 16, and the interquartile range is Q 3 minus Q 1, which is 7.5.
五数概括是二、四、七点五、十一点五、十六，四分位距等于 Q3 减 Q1，即七点五。
A box plot displays these values.
箱线图展示的就是这些数值。
A category bar chart compares categorical counts; a scatterplot needs paired quantitative measurements.
分类条形图比较的是类别计数；散点图需要成对的数量测量。
Neither directly displays this univariate five-number summary.
这两种图都不能直接展示这种单变量的五数概括。
The stated quartile convention prevents disagreement between other valid conventions.
题目规定的四分位数约定，避免了不同有效约定之间的分歧。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息作答。
Below 20 there are 2 plus 6, that is 8 of 10 observations, so 80 percent.
低于二十的有二加六，即十个观测中的八个，所以是百分之八十。
The exact observations within the bins are unknown, so no exact mean follows; midpoint estimates must be labelled as estimates.
各组内的具体观测值未知，所以算不出精确的平均数；用组中值得到的估计必须标明是估计。
A scatterplot represents pairs, and a fitted relation should describe its main shape, with the unusual point considered.
散点图表示的是成对数据，拟合的关系应当描述它的主要形状，并考虑那个异常点。
Joining every observation invents a path between separate cases and ignores the curved trend.
把每个观测点连起来，等于在彼此独立的个案之间编造了一条路径，也忽略了弯曲的趋势。
Inspect actual axis scales and the outlier before fitting or extrapolating.
在拟合或外推之前，先看清实际的坐标轴刻度和那个离群点。
Return to the task and explain why the method fits.
回到该任务，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习无法预测官方分数。
Complete required live or recorded evidence separately.
需单独完成必需的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。