数学英语 15 What Are Averages?

by Jason Marshall
In the last few articles, we’ve talked about decimals and how they’re related to fractions through the process of division. Now, it’s time to turn our attention to some practical applications of these tools. Up first today we’re talking about statistical¹ averages—in particular: batting averages.
But first, the podcast edition of this tip was sponsored by Go To Meeting. Save time and money by hosting your meetings online. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their web conferencing solution.
Who is the Best Hitter in Baseball?
Who is the best hitter in baseball? Or, if you’re not a baseball fan, feel free to replace this question with an analogous² one from the sport of your choosing. Those of you who are baseball fans probably have a favorite player. And, for many of you, this favorite player is probably also the person you claim to be the best hitter. If that’s the case, it’s also pretty likely that your opinion has been swayed by your passion. Now, there’s certainly nothing wrong with having a little passion and an opinion, but it sure would be nice if we could determine the best hitter in baseball in a way that isn’t biased⁴ by your feelings. Well, I have good news for you: there is a way—it’s called statistics.
What is Statistics?
Statistics is the set of ideas in math that deals with collecting and analyzing⁵ sets of numerical data. From analyzing poll results that tell us who is winning an election, to determining whether a person taking a lie detector⁶ test is telling the truth, statistical analysis gives us a way to understand sets of observations in a consistent and unbiased way. So let’s see how we can use it to figure out which player is the best hitter in Major League Baseball.
What is a Batting Average in Baseball?
What number should we use to determine if somebody is a good hitter? How about the total number of hits they’ve had in their career? Well, a large number of career hits could be a good sign; but there’s a problem: a mediocre⁷ player blessed with unusual longevity—and many at bats—could, over the course of sufficiently⁸ many seasons, amass⁹ a large number of hits. Clearly, it wouldn’t be fair to use total career hits to compare the skills of an average player in his tenth season to a phenomenal player in his first. We need to figure out a way to remove the bias³ introduced by the total number of at bats a player has had. In other words, a true measure of a hitter’s skill is measured not by his total number of hits, but by the rate at which he succeeds at the plate. The number we’re looking for here is called the player’s batting average.
Now, you’ve probably heard the term “batting average” before, and you’ve also probably heard game announcers make statements like “[so and so] is batting 275 this season,” but what exactly does that statement mean? Well, there’s a big clue in how batting averages appear in print—namely, the above average would not be written “275”, but would instead be written “.275”. You’ll recognize that .275 is a decimal number, which may also be thought of as a percentage. And that’s the interpretation¹⁰: batting averages in baseball represent the percentage likelihood, also known as the probability, that a batter¹¹ will succeed in getting a hit. So, a .275 batting average means that a batter hits safely 27.5% of the time—which might not sound too great, but actually isn’t bad in baseball.
How to Calculate Batting Averages
But we’re missing one very important piece of the puzzle: How are batting averages actually calculated? Well, as we discovered earlier, to compare the skills of two players, we need to take into account the total number of at bats they’ve each had to accrue¹² their hits. That is, the number we’re interested in isn’t the total number of career hits, but is instead the total number of hits divided by the total number of at bats. For example, if a player has 275 career hits in 1000 at bats, his batting average is the fraction 275/1000—275 hits per 1000 at bats. That fraction has an equivalent decimal representation of .275—which is what we call “batting 275.” So, if two players have the same number of career hits, but one of them has batted half as many times, that player’s batting average will be twice as big—and it’ll be obvious that that player is a much better hitter.
Why is Statistics Useful?
So, let’s return to our original question: Who is the best hitter in baseball? Well, there are several factors to consider (for example: are you more interested in home runs or overall hits?), but you could make a pretty good argument that the best hitter is the player with the highest batting average. After all, that’s the player who, on average, has the highest number of hits per 1000 at bats. And that is the beauty of statistics—it gives consistent and unbiased answers. It doesn’t matter who you think the best hitter is; you can use statistics to calculate the answer.

Wrap Up

Remember, you can get updates about the Math Dude podcast, the “Video Extra!” episodes posted most weeks to YouTube (this week will be an exception), and all my other guaranteed-to-be-fascinating musings about math, science, and life in general by following me on Twitter. And please join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook—it’s a wonderful way to get updates and see lots of interesting stories about math and science in the everyday world.

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

 

1 statistical   

adj.统计的，统计学的

参考例句：

• He showed the price fluctuations in a statistical table.他用统计表显示价格的波动。
• They're making detailed statistical analysis.他们正在做具体的统计分析。

2 analogous   

adj.相似的；类似的

参考例句：

• The two situations are roughly analogous.两种情況大致相似。
• The company is in a position closely analogous to that of its main rival.该公司与主要竞争对手的处境极为相似。

3 bias   

n.偏见，偏心，偏袒；vt.使有偏见

参考例句：

• They are accusing the teacher of political bias in his marking.他们在指控那名教师打分数有政治偏见。
• He had a bias toward the plan.他对这项计划有偏见。

4 biased   

a.有偏见的

参考例句：

• a school biased towards music and art 一所偏重音乐和艺术的学校
• The Methods: They employed were heavily biased in the gentry's favour. 他们采用的方法严重偏袒中上阶级。

5 analyzing   

v.分析；分析( analyze的现在分词 )；分解；解释；对…进行心理分析n.分析

参考例句：

• Analyzing the date of some socialist countries presents even greater problem s. 分析某些社会主义国家的统计数据，暴露出的问题甚至更大。 来自辞典例句
• He undoubtedly was not far off the mark in analyzing its predictions. 当然，他对其预测所作的分析倒也八九不离十。 来自辞典例句

6 detector   

n.发觉者，探测器

参考例句：

• The detector is housed in a streamlined cylindrical container.探测器安装在流线型圆柱形容器内。
• Please walk through the metal detector.请走过金属检测器。

7 mediocre   

adj.平常的，普通的

参考例句：

• The student tried hard,but his work is mediocre. 该生学习刻苦，但学业平庸。
• Only lazybones and mediocre persons could hanker after the days of messing together.只有懒汉庸才才会留恋那大锅饭的年代。

8 sufficiently   

adv.足够地，充分地

参考例句：

• It turned out he had not insured the house sufficiently.原来他没有给房屋投足保险。
• The new policy was sufficiently elastic to accommodate both views.新政策充分灵活地适用两种观点。

9 amass   

vt.积累，积聚

参考例句：

• How had he amassed his fortune?他是如何积累财富的呢？
• The capitalists amass great wealth by exploiting workers.资本家剥削工人而积累了巨额财富。

10 interpretation   

n.解释，说明，描述；艺术处理

参考例句：

• His statement admits of one interpretation only.他的话只有一种解释。
• Analysis and interpretation is a very personal thing.分析与说明是个很主观的事情。

11 batter   

v.接连重击；磨损；n.牛奶面糊；击球员

参考例句：

• The batter skied to the center fielder.击球手打出一个高飞球到中外野手。
• Put a small quantity of sugar into the batter.在面糊里放少量的糖。

12 accrue   

v.(利息等)增大，增多

参考例句：

• Ability to think will accrue to you from good habits of study.思考能力将因良好的学习习惯而自然增强。
• Money deposited in banks will accrue to us with interest.钱存在银行，利息自生。

13 subscribe   

vi.(to)订阅，订购；同意；vt.捐助，赞助

参考例句：

• I heartily subscribe to that sentiment.我十分赞同那个观点。
• The magazine is trying to get more readers to subscribe.该杂志正大力发展新订户。