六百名选手参加了比赛。
最快的选手用了 8 分钟完成比赛，而最慢的选手用了 18 分钟。
点 (8, 1)、(15, 300)、(17, 450) 和 (18, 600) 是上方网格所示选手的累积频数曲线上的点。已知比赛时间的四分位距为 4 分钟。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Find the cumulative frequency corresponding to the lower quartile.

There are $600$ runners.

Lower quartile cumulative frequency:
$\frac{1}{4}\times 600=150$

2. Use the given interquartile time to find the lower quartile time.

The upper quartile has cumulative frequency
$\frac{3}{4}\times 600=450.$

The point $(17,450)$ is given on the cumulative frequency curve, so
$Q_3=17.$

Given interquartile time is $4$ minutes,
$Q_3-Q_1=4$
$17-Q_1=4$
$Q_1=13.$

Hence the lower quartile point is
$(13,150).$

答案

$(13, 150)$

1. Identify all points that the cumulative frequency curve must pass through.

From part (i), the lower quartile point is $(13,150)$ .

The given points are $(8,1)$ , $(15,300)$ , $(17,450)$ and $(18,600)$ .

So plot the points
$(8,1),\ (13,150),\ (15,300),\ (17,450),\ (18,600).$

2. Draw the cumulative frequency curve through the plotted points.

Join the plotted points with a smooth, non-decreasing curve.

The curve should start near the fastest time at $8$ minutes and rise to cumulative frequency $600$ at $18$ minutes.

答案

A smooth increasing cumulative frequency curve passing through $(8,1)$ , $(13,150)$ , $(15,300)$ , $(17,450)$ and $(18,600)$ .

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