Comparing Data Sets with Averages and Range | 利用平均数、中位数、众数与极差比较数据集

📚 Comparing Data Sets with Averages and Range | 利用平均数、中位数、众数与极差比较数据集

In KS3 Cambridge Mathematics, data handling questions often ask you to compare two sets of data. A good comparison uses at least one average and the range. This article will help you revise the key skills and write clear, exam-style answers.

在 KS3 剑桥数学中，数据处理题经常要求你比较两组数据。一个好的比较至少要使用一个平均数和极差。本文将帮助你复习关键技能，并写出清晰、符合考试要求的答案。

1. Mean, Median, Mode and Range Recap | 平均数、中位数、众数和极差回顾

The mean is found by adding all the data values and dividing by the number of values. The median is the middle value when the data are placed in ascending order. The mode is the value that occurs most often. The range is the largest value minus the smallest value.

平均数的求法是将所有数据值相加，再除以数据的个数。中位数是将数据按从小到大的顺序排列后位于中间位置的值。众数是出现次数最多的值。极差是最大值减去最小值。

Mean = Σx ÷ n Range = xₘₐₓ − xₘᵢₙ

For example, for the data set 4, 7, 8, 8, 12: mean = (4 + 7 + 8 + 8 + 12) ÷ 5 = 7.8, median = 8, mode = 8, range = 12 − 4 = 8.

例如，对于数据集 4、7、8、8、12：平均数 = (4 + 7 + 8 + 8 + 12) ÷ 5 = 7.8，中位数 = 8，众数 = 8，极差 = 12 − 4 = 8。

If the number of data values is even, the median is the mean of the two middle values. For example, in the set 3, 5, 7, 9, the median is (5 + 7) ÷ 2 = 6.

如果数据的个数为偶数，中位数就是两个中间值的平均数。例如，在数据集 3、5、7、9 中，中位数为 (5 + 7) ÷ 2 = 6。

2. Calculating the Mean from a Frequency Table | 从频数表计算平均数

When data are shown in a frequency table, multiply each value by its frequency, add the products, then divide by the total frequency. The total frequency is Σf, and the sum of the products is Σ(fx).

当数据以频数表的形式给出时，将每个数值乘以它的频数，把所有乘积相加，再除以总频数。总频数为 Σf，所有乘积之和为 Σ(fx)。

Mean = Σ(fx) ÷ Σf

Example: values x = 1, 2, 3, 4 with frequencies f = 3, 5, 2, 1. Then Σf = 3 + 5 + 2 + 1 =

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