题目
Each year the total number of hours, , of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.
| Number of years | 4 | 8 | 14 | 25 | 7 | 2 |
(a) Draw a cumulative frequency graph to illustrate the data.
(b) Use your graph to estimate the 70th percentile of the data.
(c) Calculate an estimate for the mean number of hours of sunshine in Kintoo during June over the last 60 years.
题目中文翻译
每年记录 Kintoo 在 6 月的日照总时数 。过去 60 年的结果汇总于下表。
| 年数 | 4 | 8 | 14 | 25 | 7 | 2 |
(a) 画一条累积频数曲线表示这些数据。
(b) 利用你所画的图估计这些数据的第 70 百分位数。
(c) 计算过去 60 年 Kintoo 在 6 月的日照总时数均值的估计值。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
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累计频数逐组相加，从最低组界30对应0开始画曲线。
答题过程
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The cumulative frequencies at the upper class boundaries are
Plot
Join the points with a smooth increasing curve. Label the horizontal axis “Hours of sunshine” and the vertical axis “Cumulative frequency”, using linear scales.
(b)
解法一
思路
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第70百分位数对应60年的70%，即累计频数42。
答题过程
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The required cumulative frequency is
Read horizontally from 42 to the curve and then down to the sunshine axis. The estimate is 126 hours.
(c)
解法一
思路
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各组用中点45、75、100、125、160、210，计算加权平均。
答题过程
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The estimated mean is