2022年省考：辨析平均数增长量和增长率

在行测考试中，资料分析主要考查的是对统计材料的理解、把握、查找比较的能力，而资料分析近些年来，对于平均数相关知识点的考察越发的重视，但是由于而均数本身难度比较大，公式以及相关计算比较复杂，成为许多考生比较头疼的问题。其实对于平均数而言，也有许多小的技巧，只要掌握了计算方法、理解了题干的本质，就可以达到迅速解题的目的。今天湖北公务员考试网（http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg）就带大家一起来学习资料分析的一个重要考点——平均数的增长量和增长率。

一、基本概念

基本概念：平均数增长量是指现期平均数相对于基期平均数所增长的量;

平均数增长率则指的是现期平均数相对于基期平均数所增长的百分比。

区别：通过概念我们可以了解到，由于平均数本身是一个带单位的具体的量，因此平均数的增长量也是一个量且单位不发生变化，而平均数的增长率则是具体量的增长率，是一个百分数的形式。

二、基本公式

http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110333281.png />

三、解题及计算方法

1)平均数增长量

例1

问题：与2018年相比，2019 年全国商品房销售均价约：

A.增长 580 元

B.增长 710 元

C.下降 580 元

D.下降 710 元

【答案】A。首先确定考点，全国商品房销售均价为平均数，出现了选项为增长或者下降且带单位，因此所求为平均数的增长量，而所求为全国商品房销售均价，销售额为总量，面积为份数。全国商品房销售面积和销售额分别为171558万平方米和159725亿元，同比分别增长-0.1%和6.5%，因此列式为http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110217863.png />故排除C,D选项。由于选项数量级相同，我们在计算时只需要计算结果的有效数字即可，6.5%-(-0.1%)=6.6%，而http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110117967.png />略小于1，因此6.6%乘一个略小于1的数，一定变小，因此其有效数字应比6.6%的有效数字略小，选则稍小的A项。

小结：求平均数的增长量时，我们可类比比重的增长量计算方式，通过计算结果的有效数字结合选项排除错误答案来选择正确答案。

2)平均数增长率

例2

问题：2007-2018 年，全国茶园面积首次超过 200 万公顷的年份，当年茶园单位面积茶叶产量比上年：

A.增加了不到 10%

B.增加了 10%以上

C.下降了不到 10%

D.下降了 10%以上

【答案】A。由图形材料可知，2007-2018年全国茶园面积首次超过200万公顷的是2011年，当年茶叶产量为160.8万吨，茶园面积为205.6万公顷，则茶园单位面积茶叶产量为http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110237336.png />2010年茶园单位面积茶叶产量为http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110815296.png />所求为园单位面积茶叶产量比上年增加的百分数，为平均数的增长率，由于题干中未出现增长率，因此需用原始公式http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110385568.png />求解，代入数据列式为http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110797530.png />故选A。

小结：

1)求平均数的增长率时，如果选项是精确的数值且给定了总量和份数的增长率，可直接套公式http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110129245.png />若选项为精确数没有给出总量和份数的增长率，而是分别给出了现期和基期的总量和份数，则要套用原始公式http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110246798.png />求解。

2)求平均数的增长率时，若选项为一个范围且没有给出总量和份数的增长率，而是分别给出了现期和基期的总量和份数时，可采用估算的方式，分别计算总量和份数的增长率，再代入原始公式http://www.hbrsks.net/zb_users/upload/water/2022-01-10/61dc082663378.jpeg/zb_users/upload/water/2022-01-10/61dc082373319.jpeg/zb_users/upload/water/2022-01-10/61dc081eced8b.jpeg/zb_users/upload/water/2022-01-10/61dc081aefc23.jpeg/zb_users/upload/water/2022-01-10/61dc08180b3da.jpeg/zb_users/upload/water/2022-01-10/61dc0815c7f3c.jpeg/zb_users/upload/water/2022-01-10/61dc0813489d0.jpeg/zb_users/upload/water/2022-01-10/61dc0812b23bd.jpeg/zb_users/upload/water/2022-01-10/61dc08112be16.jpeg/zb_users/upload/water/2022-01-10/61dc0810a162a.jpeg/zb_users/upload/water/2022-01-10/61dc081026774.jpeg/zb_users/upload/water/2022-01-10/61dc080f00f80.jpeg/zb_users/upload/water/2022-01-10/61dc080c8041a.jpeg/uploadfile2013/image/20220110538387.png />去计算。

以上是平均数增长量和增长率相关的公式以及解题技巧。希望对大家的备考有所帮助，也希望大家在今后的练习中灵活应用，提高做题速度以及正确率。