问题 单项选择题

在表6-1中,第1行依次列出了0.00,0.01,0.02,0.03,…,0.99,共100个数据;对第1行的每个数据采用方法1(通常的4舍5入法)处理后形成第2行数据;对第1行的每个数据采用方法2(修改后的4舍5入法)处理后形成第3行数据。

表6-1 数据处理表

原数据0.000.040.050.060.140.150.160.240.250.340.350.99
方法1处理结果0.00.00.10.10.10.20.20.20.30.30.40.99
方法2处理结果0.00.00.00.10.10.20.20.20.20.30.40.99

答案

参考答案:C

解析:
[要点解析] 对于表6-1的处理方法1,是对末位数字采用四舍五入处理,即末位数字是4或4以下时舍去,若末位数字是5或5以上,则进1。这种做法确实简单实用,但从表6-4可以看出,对平均而言,舍的量略低于入的量。

表6-4 数据处理

原数据 0.00.10.20.30.40.50.60.70.80.9
4舍5入处理结果0000011111
变化量0-0.1-0.2-0.3-0.4+0.5+0.4+0.3+0.2+0.1

其中,0.4舍的量与0.6入的量可以相抵,0.3舍的量与0.7入的量可以相抵……。正数4舍5入的偏差来自尾数为5的量都要进位,从而产生偏高结果。如果是在银行利息计算中,采用这种粗略的舍入方法将会有较大一笔钱的出入。为平衡起见,应将尾数为5的情况分裂成两种情况:有一半的可能要舍,有一半的可能需要入。
方法2对四舍五入法做了如下修改:如果末位数字是5,则并不总是入,而需要根据前一位数字的奇偶性再决定舍入,如果前一位数字是偶数,则将5舍去;如果前一位数字是奇数,则进1。例如,0.05将舍入成0.0;0.15将舍入成0.2。这一舍一入的偏差量刚好相抵。因此对表6-1第3行数据求算术平均值,不会产生统计偏差现象。
换个思路考虑问题,单纯解答本题并不难。表6-1第1行数据都是正数,均匀地列出了2位小数的各种可能,其平均值为49.50。经方法1处理后的100个数据的平均值为50.00,可以看出,方法1产生了偏高结果;经方法2处理后的100个数据的平均值为49.50,可以看出,方法2改进了方法1。
另外,对于正负数对称分布的情况,则四舍五入法不会产生偏差。因为正数的舍(引起减少)与负数的舍(引起增加)相抵,正数的入(引起增加)与负数的入(引起减少)相抵。

单项选择题 A2型题
阅读理解

阅读理解。

     A lot of us lose life's tough battles by starting a frontal attack-when a touch of humor might well enable

us to win. Consider the case of a young friend of mine, who hit a traffic jam on his way to work shortly

after receiving an ultimatum (最后通牒) about being late on the job. Although there was a good reason for

Sam's being late-serious illness at home-he decided that this by-now-familiar excuse wouldn't work any

longer. His supervisor was probably already pacing up and down preparing a dismissal speech.

     Yes, the boss was. Sam entered the office at 9:35. The place was as quiet as a locker room; everyone

was hard at work. Sam's supervisor came up to him. Suddenly, Sam forced a grin and stretched out his

hand. "How do you do!" he said. "I'm Sam Maynard. I'm applying for a job, which, I understand, became

available just 35 minutes ago. Does the early bird get the worm?"

     The room exploded in laughter. The supervisor clamped off a smile and walked back to his office. Sam

Maynard had saved his job-with the only tool that could win, a laugh.

     Humor is a most effective, yet frequently neglected, means of handling the difficult situations in our lives.

It can be used for patching up differences, apologizing, saying "no", criticizing, getting the other fellow to

do what you want without his losing face. For some jobs, it's the only tool that can succeed. It is a way to

discuss subjects so sensitive that serious dialog may start a quarrel. For example, many believe that comedians

on television are doing more today for racial and religious tolerance than people in any other forum.

1. Why was Sam late for his job?

A. Because he was ill.

B. Because he was caught in a traffic jam.

C. He was busy applying for a new job.

D. Because he got up late.

2. The phrase "clamped off" in Paragraph 3 means ____.

A. burst into

B. tried to set up

C. tried to hold back

D. gave out

3. Which of the following statements can we infer from the passage?

A. Sam was supposed to come to his office at 8:30.

B. It wasn't the first time that Sam came late for his work.

C. Humor is the most effective way of solving problems.

D. All people lose life's battles for they are lacking in a sense of humor.