Statistik
AQA · GCSE · Mathematics Topik 6 4:31 Narasi bahasa Inggris · Subtitle bahasa Inggris + 中文 disematkan langsung
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Four families carry statistics.
统计有四类要点。
The mean is the sum of f x over the sum of f, using midpoints for grouped data; the median and mode are the other centres.
平均数是 Σfx ÷ Σf，分组数据用组中值；中位数和众数是另外的集中量。
Spread is the range or the interquartile range.
离散程度用极差或四分位距。
A pie angle is f over n times 360, and histogram height is frequency density.
饼图角度是 f/n × 360°，直方图高度是频率密度。
Scatter graphs show correlation and a line of best fit.
散点图显示相关性和最佳拟合线。
Take a random sample of 80 students: 24 walk to school.
随机抽取 80 名学生：24 人步行上学。
That proportion is 24 over 80, which is 0.3.
比例是 24/80 = 0.3。
Apply it to a school of 600: about 180 walkers.
用到 600 人的学校：约 180 人步行。
It is an estimate, not a count; another sample would give a slightly different answer.
这是估计，不是清点；换一个样本，答案会略有不同。
Compare three samples.
比较三种样本。
With random selection, no one is left out on purpose.
随机抽样不会故意漏掉任何人。
A sports club overrepresents active students, so it misses the less active ones.
体育俱乐部样本偏向爱运动的学生，漏掉不爱运动的。
A voluntary online poll misses people who do not reply, however many answers arrive.
自愿网上调查漏掉不回复的人，无论收到多少回复。
And every sample, even a random one, has sampling variability.
而每个样本，即使是随机样本，都有抽样波动。
40 students travel to school: 10 walking, 15 by bus and 15 cycling.
40 名学生上学方式：10 人步行，15 人坐公交，15 人骑车。
The whole circle, 360 degrees, shares out over 40 people, so each student is 9 degrees.
整圆 360° 分给 40 人，每人 9°。
10 walkers make 90 degrees; 15 by bus make 135, and 15 cycling make 135 too.
步行 10 人是 90°；公交 15 人是 135°，骑车 15 人也是 135°。
Check: they add to 360.
检验：加起来是 360°。
In a histogram, area is frequency, so the height is frequency density: frequency divided by class width.
在直方图中，面积代表频数，所以高度是频数密度：频数除以组距。
Classes 0 to 10, 10 to 20 and 20 to 40 with frequencies 20, 30 and 20 have densities 2, 3 and 1.
0 到 10、10 到 20、20 到 40 三组，频数分别是 20、30、20，密度分别是 2、3、1。
The wide last bar is the shortest, yet it still holds 20.
最宽的最后一个长条最矮，但仍然包含 20 个。
Cumulative frequency plots at the upper class boundaries, and the median of 70 values reads at 35, which interpolates to 15.
累积频数在上组界处描点，70 个数据的中位数在第 35 个读取，插值得 15。
Plot the running total at each upper boundary: 0, 20, 50 and 70.
在每个上组界处描出累计数：0、20、50、70。
With 70 values, the median sits at 35.
共 70 个数据，中位数在第 35 个。
Read across at 35 and down: the median is 15.
从 35 横读再向下：中位数是 15。
Q1 reads at 17.5 and gives 8.75; Q3 reads at 52.5 and gives 22.5.
Q1 在 17.5 处读得 8.75；Q3 在 52.5 处读得 22.5。
So the interquartile range is 13.75.
所以四分位距是 13.75。
Plot five values: 2, 4, 4, 6 and 24.
画出五个数：2、4、4、6、24。
The total is 40, so the mean is 8, but four of the five values lie below it.
总和 40，平均数 8，但五个数中有四个都比它小。
The unusual value 24 drags the mean to 8, while the median stays 4.
异常值 24 把平均数拉到 8，而中位数仍是 4。
For data with an outlier, the median is the better typical value.
有异常值时，中位数更能代表典型值。
Use exact products for a grouped mean: 108 plus 136.8 plus 56 is 300.8, and over 40 that is 7.52.
分组平均数要用精确的乘积：108 加 136.8 加 56 等于 300.8，除以 40 得 7.52。
An extreme value moves the mean but not the median: in 2, 4, 4, 6, 24 the mean is 8 but the median stays 4.
极端值会改变平均数，但不改变中位数：在 2、4、4、6、24 中，平均数 是 8，中位数仍是 4。
A box plot shows five numbers: the minimum 2.4, the lower quartile 4, the median 6, the upper quartile 7 and the maximum 9.
箱线图显示五个数：最小值 2.4、下四分位数 4、中位数 6、上四分位数 7、最大值 9。
The interquartile range is 7 minus 4, which is 3.
四分位距是 7 减 4，等于 3。
Correlation can be positive, negative or absent; strong or weak describes how tightly the points cluster, not how steep they are.
相关可以是正相关、负相关或不相关；强或弱描述的是点聚集的紧密程度，而不是陡峭程度。
Correlation does not show causation.
相关不代表因果。
A line of best fit balances the points.
最佳拟合线要平衡各个点。
With y hat equals 40 plus 4.5 x observed for inputs 1 to 5, predicting at 3.6 gives 56.2, an interpolation.
观测输入为 1 到 5，拟合线 y 帽等于 40 加 4.5x，在 3.6 处的预测是 56.2，这是内插。
At 10 the line gives 85, but that is an extrapolation, and the trend may flatten.
在 10 处直线给出 85，但那是外推，趋势可能变平。
Check yourself.
自我检测。
2 plus 10 plus 9 is 21, over 10: a mean of 2.1.
2 + 10 + 9 = 21，除以 10：平均数 2.1。
Frequency 20 over width 20 gives a density of 1.
频数 20 除以组宽 20，密度 1。
30 out of 120 is a quarter of the pie: 90 degrees.
120 中的 30 是饼图的四分之一：90°。
Quartiles 12 and 21 give an IQR of 9.
四分位数 12 和 21，四分位距 9。
And correlation shows association, never cause on its own.
相关性只表示关联，单凭它不能证明因果。