电大统计学原理考试必备小抄(计算题)

1、统计学原理复习（计算题） 1某单位40名职工业务考核成绩分别为: 68 89 88 84 86 87 75 73 72 68 75 82 97 58 81 54 79 76 95 76 71 60 90 65 76 72 76 85 89 92 64 57 83 81 78 77 72 61 70 81单位规定：60分以下为不及格,6070分为及格,7080分为中,8090分为良,90100分为优。要求：(1)将参加考试的职工按考核成绩分为不及格、及格、中、良、优五组并编制一张考核成绩次数分配表；（2）指出分组标志及类型及采用的分组方法；（3）计算本单位职工业务考核平均成绩（4）分析本单位职工

2、业务考核情况。解：（1）成 绩职工人数频率(%)60分以下60-7070-8080-9090-10036151247.51537.53010合 计40100 （2）分组标志为成绩,其类型为数量标志；分组方法为：变量分组中的开放组距式分组,组限表示方法是重叠组限；（3）本单位职工业务考核平均成绩（4）本单位的职工考核成绩的分布呈两头小, 中间大的 正态分布的形态，说明大多数职工对业务知识的掌握达到了该单位的要求。22004年某月份甲、乙两农贸市场农产品价格和成交量、成交额资料如下：品种价格（元/斤）甲市场成交额（万元）乙市场成交量（万斤）甲乙丙211合计5.5

3、4试问哪一个市场农产品的平均价格较高？并说明原因。解： 品种价格（元）X甲市场乙市场成交额成交量成交量成交额mm/xfxf甲乙丙1212合计5.5445.3解：先分别计算两个市场的平均价格如下：甲市场平均价格（元/斤） 乙市场平均价格（元/斤） 说明：两个市场销售单价是相同的，销售总量也是相同的，影响到两个市场平均价格高低不同的原因就在于各种价格的农产品在两个市场的成交量不同。 3某车间有甲、乙两个生产组，甲组平均每个工人的日产量为36件，标准差为9.6件；乙组工人日产量资料如下：日产量（件）工人数（人）1525354515383413

4、要求：计算乙组平均每个工人的日产量和标准差； 比较甲、乙两生产小组哪个组的日产量更有代表性？ 解：（1）（件） （件） （2）利用标准差系数进行判断： 因为0.305 0.267故甲组工人的平均日产量更有代表性。 4某工厂有1500个工人，用简单随机重复抽样的方法抽出50个工人作为样本，调查其月平均产量水平，得每人平均产量560件，标准差32.45要求：（1）计算抽样平均误差（重复与不重复）； （2）以95%的概率（z=1.96）估计该厂工人的月平均产量的区间；（3）以同样的概率估计该厂工人总产量的区间。 解： （1） 重复抽样： 不重复抽样： （2）抽样极限误差 = 1.964.59 =9件

5、月平均产量的区间： 下限: =560-9=551件 上限:=560+9=569件 （3）总产量的区间：（5511500 826500件； 5691500 853500件） 5采用简单随机重复抽样的方法，在2000件产品中抽查200件，其中合格品190件.要求：（1）计算合格品率及其抽样平均误差（2）以95.45%的概率保证程度（z=2）对合格品率和合格品数量进行区间估计。（3）如果极限误差为2.31%，则其概率保证程度是多少？ 解：(1)样本合格率p = n1n = 190200 = 95% 抽样平均误差 = 1.54%(2)抽样极限误差p=zp = 21.54% = 3.08%下限:p=95

6、%-3.08% = 91.92%上限:p=95%+3.08% = 98.08% 则：总体合格品率区间：（91.92% 98.08%） 总体合格品数量区间（91.92%2000=1838件 98.08%2000=1962件） (3)当极限误差为2.31%时，则概率保证程度为86.64% (z=) 6 某企业上半年产品产量与单位成本资料如下：月 份产量（千件）单位成本（元）123456234345737271736968要求：（）计算相关系数，说明两个变量相关的密切程度。 （）配合回归方程，指出产量每增加1000件时，单位成本平均变动多少？ （）假定产量为6000件时，单位成本为多少元？解：计算相

7、关系数时，两个变量都是随机变量，不须区分自变量和因变量。考虑到要配和合回归方程，所以这里设产量为自变量（），单位成本为因变量（）月份产量（千件）单位成本（元）123456234345737271736968491691625532951845041532947614624146216284219276340合 计2142679302681481 （）计算相关系数：说明产量和单位成本之间存在高度负相关。（）配合回归方程 =-1.82 =77.37 回归方程为：.产量每增加1000件时，单位成本平均减少.元（）当产量为件时，即，代入回归方程：.（元） 7根据企业产品销售额(万元)和销售利润率(%)

8、资料计算出如下数据: n=7 =1890 =31.1 2=535500 2=174.15 =9318 要求: (1) 确定以利润率为因变量的直线回归方程. (2)解释式中回归系数的经济含义. (3)当销售额为500万元时,利润率为多少? 解：（1）配合直线回归方程： b= = =0.0365 a= =-5.41 则回归直线方程为： yc=-5.41+0.0365x （2）回归系数b的经济意义：当销售额每增加一万元，销售利润率增加0.0365% （3）计算预测值： 当x=500万元时 yc=-5.41+0.0365=12.8% 8 某商店两种商品的销售资料如下：商品单位销售量单价（元）基期计算期

9、基期计算期甲乙件公斤50150601608121014要求：（1）计算两种商品销售额指数及销售额变动的绝对额；（2）计算两种商品销售量总指数及由于销售量变动影响销售额的绝对额；（3）计算两种商品销售价格总指数及由于价格变动影响销售额的绝对额。 解：（1）商品销售额指数= 销售额变动的绝对额：元 （2）两种商品销售量总指数= 销售量变动影响销售额的绝对额元 （3）商品销售价格总指数= 价格变动影响销售额的绝对额：元 9某商店两种商品的销售额和销售价格的变化情况如下：商品单位销售额（万元）1996年比1995年销售价格提高（%）1995年1996年甲乙米件12040130361012要求：(1)计

10、算两种商品销售价格总指数和由于价格变动对销售额的影响绝对额。 (2)计算销售量总指数,计算由于销售量变动，消费者增加（减少）的支出金额。解：（1）商品销售价格总指数= 由于价格变动对销售额的影响绝对额：万元 （2）)计算销售量总指数:商品销售价格总指数=而从资料和前面的计算中得知： 所以：商品销售量总指数=，由于销售量变动，消费者增加减少的支出金额: - 10某地区1984年平均人口数为150万人，1995年人口变动情况如下：月份1369次年1月月初人数102185190192184计算：（1）1995年平均人口数;（2）1984-1995年该地区人口的平均增长速度.解：（1）1995年平均人

11、口数=181.38万人（2）1984-1995年该地区人口的平均增长速度： 11某地区19951999年粮食产量资料如下：年份1995年1996年1997年1998年1999年粮食产量（万斤）434472516584618要求：（1）计算各年的逐期增长量、累积增长量、环比发展速度、定基发展速度；（2）计算1995年-1999年该地区粮食产量的年平均增长量和粮食产量的年平均发展速度；（3）如果从1999年以后该地区的粮食产量按8%的增长速度发展，2005年该地区的粮食产量将达到什么水平？ 解：（1）年 份1995年1996年1997年1998年1999年粮食产量（万斤） 环比发展速度 定基发展速

12、度逐期增长量累积增长量434-4721087610876383851610932118894482584113181345668150618105821424034184平均增长量=（万斤）（万斤） （2）平均发展速度（3）=980.69（万斤） 12年 份1995年1996年1997年1998年1999年粮食产量（万斤） 环比发展速度 逐期增长量 434- 10876 44 68 10582 要求：（1）计算各年的逐期增长量、累积增长量、环比发展速度、定基发展速度；（2）计算1995年-1999年该地区粮食产量的年平均增长量和粮食产量的年平均发展速度；（3）如果从1999年以后该地区的粮食产

13、量按8%的增长速度发展，2005年该地区的粮食产量将达到什么水平？ （做法见上题）请您删除一下内容，O(_)O谢谢！2016年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄Basketball can make a true claim to being the only major sport that is an American invention. From high school to the professional level, basketball attracts a large following for live games as well as t

14、elevision coverage of events like the National Collegiate Athletic Association (NCAA) annual tournament and the National Basketball Association (NBA) and Womens National Basketball Association (WNBA) playoffs. And it has also made American heroes out of its player and coach legends like Michael Jord

15、an, Larry Bird, Earvin Magic Johnson, Sheryl Swoopes, and other great players. At the heart of the game is the playing space and the equipment. The space is a rectangular, indoor court. The principal pieces of equipment are the two elevated baskets, one at each end (in the long direction) of the cou

16、rt, and the basketball itself. The ball is spherical in shape and is inflated. Basket-balls range in size from 28.5-30 in (72-76 cm) in circumference, and in weight from 18-22 oz (510-624 g). For players below the high school level, a smaller ball is used, but the ball in mens games measures 29.5-30

17、 in (75-76 cm) in circumference, and a womens ball is 28.5-29 in (72-74 cm) in circumference. The covering of the ball is leather, rubber, composition, or synthetic, although leather covers only are dictated by rules for college play, unless the teams agree otherwise. Orange is the regulation color.

18、 At all levels of play, the home team provides the ball. Inflation of the ball is based on the height of the balls bounce. Inside the covering or casing, a rubber bladder holds air. The ball must be inflated to a pressure sufficient to make it rebound to a height (measured to the top of the ball) of

19、 49-54 in (1.2-1.4 m) when it is dropped on a solid wooden floor from a starting height of 6 ft (1.80 m) measured from the bottom of the ball. The factory must test the balls, and the air pressure that makes the ball legal in keeping with the bounce test is stamped on the ball. During the intensity

20、of high school and college tourneys and the professional playoffs, this inflated sphere commands considerable attention. Basketball is one of few sports with a known date of birth. On December 1, 1891, in Springfield, Massachusetts, James Naismith hung two half-bushel peach baskets at the opposite e

21、nds of a gymnasium and out-lined 13 rules based on five principles to his students at the International Training School of the Young Mens Christian Association (YMCA), which later became Springfield College. Naismith (1861-1939) was a physical education teacher who was seeking a team sport with limi

22、ted physical contact but a lot of running, jumping, shooting, and the hand-eye coordination required in handling a ball. The peach baskets he hung as goals gave the sport the name of basketball. His students were excited about the game, and Christmas vacation gave them the chance to tell their frien

23、ds and people at their local YMCAs about the game. The association leaders wrote to Naismith asking for copies of the rules, and they were published in the Triangle, the school newspaper, on January 15,1892. Naismiths five basic principles center on the ball, which was described as large, light, and

24、 handled with the hands. Players could not move the ball by running alone, and none of the players was restricted against handling the ball. The playing area was also open to all players, but there was to be no physical contact between players; the ball was the objective. To score, the ball had to b

25、e shot through a horizontal, elevated goal. The team with the most points at the end of an allotted time period wins. Early in the history of basketball, the local YMCAs provided the gymnasiums, and membership in the organization grew rapidly. The size of the local gym dictated the number of players

26、; smaller gyms used five players on a side, and the larger gyms allowed seven to nine. The team size became generally established as five in 1895, and, in 1897, this was made formal in the rules. The YMCA lost interest in supporting the game because 10-20 basketball players monopolized a gymnasium p

27、reviously used by many more in a variety of activities. YMCA membership dropped, and basketball enthusiasts played in local halls. This led to the building of basketball gymnasiums at schools and colleges and also to the formation of professional leagues. Although basketball was born in the United S

28、tates, five of Naismiths original players were Canadians, and the game spread to Canada immediately. It was played in France by 1893; England in 1894; Australia, China, and India between 1895 and 1900; and Japan in 1900. From 1891 through 1893, a soccer ball was used to play basketball. The first ba

29、sketball was manufactured in 1894. It was 32 in (81 cm) in circumference, or about 4 in (10 cm) larger than a soccer ball. The dedicated basketball was made of laced leather and weighed less than 20 oz (567 g). The first molded ball that eliminated the need for laces was introduced in 1948; its cons

30、truction and size of 30 in (76 cm) were ruled official in 1949. The rule-setters came from several groups early in the 1900s. Colleges and universities established their rules committees in 1905, the YMCA and the Amateur Athletic Union (AAU) created a set of rules jointly, state militia groups abide

31、d by a shared set of rules, and there were two professional sets of rules. A Joint Rules Committee for colleges, the AAU, and the YMCA was created in 1915, and, under the name the National Basketball Committee (NBC) made rules for amateur play until 1979. In that year, the National Federation of Sta

32、te High School Associations began governing the sport at the high school level, and the NCAA Rules Committee assumed rule-making responsibilities for junior colleges, colleges, and the Armed Forces, with a similar committee holding jurisdiction over womens basketball. Until World War II, basketball

33、became increasingly popular in the United States especially at the high school and college levels. After World War II, its popularity grew around the world. In the 1980s, interest in the game truly exploded because of television exposure. Broadcast of the NCAA Championship Games began in 1963, and,

34、by the 1980s, cable television was carrying regular season college games and even high school championships in some states. Players like Bill Russell, Wilt Chamberlain, and Lew Alcindor (Kareem Abdul-Jabbar) became nationally famous at the college level and carried their fans along in their professi

35、onal basketball careers. The womens game changed radically in 1971 when separate rules for women were modified to more closely resemble the mens game. Television interest followed the women as well with broadcast of NCAA championship tourneys beginning in the early 1980s and the formation of the WNB

36、A in 1997. Internationally, Italy has probably become the leading basketball nation outside of the United States, with national, corporate, and professional teams. The Olympics boosts basketball internationally and has also spurred the womens game by recognizing it as an Olympic event in 1976. Again

37、, television coverage of the Olympics has been exceptionally important in drawing attention to international teams. The first professional mens basketball league in the United States was the National Basketball League (NBL), which debuted in 1898. Players were paid on a per-game basis, and this leag

38、ue and others were hurt by the poor quality of games and the ever-changing players on a team. After the Great Depression, a new NBL was organized in 1937, and the Basketball Association of America was organized in 1946. The two leagues came to agree that players had to be assigned to teams on a cont

39、ract basis and that high standards had to govern the game; under these premises, the two joined to form the National Basketball Association (NBA) in 1949. A rival American Basketball Association (ABA) was inaugurated in 1967 and challenged the NBA for college talent and market share for almost ten y

40、ears. In 1976, this league disbanded, but four of its teams remained as NBA teams. Unification came just in time for major television support. Several womens professional leagues were attempted and failed, including the Womens Professional Basketball League (WBL) and the Womens World Basketball Asso

41、ciation, before the WNBA debuted in 1997 with the support of the NBA. James Naismith, originally from Al-monte, Ontario, invented basketball at the International YMCA Training School in Springfield, Massachusetts, in 1891. The game was first played with peach baskets (hence the name) and a soccer ba

42、ll and was intended to provide indoor exercise for football players. As a result, it was originally a rough sport. Although ten of Naismiths original thirteen rules remain, the game soon changed considerably, and the founder had little to do with its evolution. The first intercollegiate game was pla

43、yed in Minnesota in 1895, with nine players to a side and a final score of nine to three. A year later, the first five-man teams played at the University of Chicago. Baskets were now constructed of twine nets but it was not until 1906 that the bottom of the nets were open. In 1897, the dribble was f

44、irst used, field goals became two points, foul shots one point, and the first professional game was played. A year later, the first professional league was started, in the East, while in 1900, the first intercollegiate league began. In 1910, in order to limit rough play, it was agreed that four foul

45、s would disqualify players, and glass backboards were used for the first time. Nonetheless, many rules still differed, depending upon where the games were played and whether professionals, collegians, or YMCA players were involved. College basketball was played from Texas to Wisconsin and throughout

46、 the East through the 1920s, but most teams played only in their own regions, which prevented a national game or audience from developing. Professional basketball was played almost exclusively in the East before the 1920s, except when a team would barnstorm into the Midwest to play local teams, ofte

47、n after a league had folded. Before the 1930s very few games, either professional or amateur, were played in facilities suitable for basketball or with a perfectly round ball. Some were played in arenas with chicken wire separating the players from fans, thus the word cagers, others with posts in th

48、e middle of the floor and often with balconies overhanging the corners, limiting the areas from which shots could be taken. Until the late 1930s, all players used the two-hand set shot, and scores remained low. Basketball in the 1920s and 1930s became both more organized and more popular, although i

49、t still lagged far behind both baseball and college football. In the pros, five urban, ethnic teams excelled and played with almost no college graduates. They were the New York Original Celtics; the Cleveland Rosenblums, owned by Max Rosenblum; Eddie Gottliebs Philadelphia SPHAs (South Philadelphia

50、Hebrew Association); and two great black teams, the New York Renaissance Five and Abe Sapersteins Harlem Globetrotters, which was actually from Chicago. While these teams had some notable players, no superstars, such as Babe Ruth, Jack Dempsey, or Red Grange, emerged to capture the publics attention

51、 as they did in other sports of the period. The same was true in college basketball up until the late 1930s, with coaches dominating the game and its development. Walter Doc Meanwell at Wisconsin, Forrest Phog Allen at Kansas, Ward Piggy Lambert at Purdue, and Henry Doc Carlson at Pittsburgh all mad

52、e significant contributions to the games development: zone defenses, the weave, the passing game, and the fast break. In the decade preceding World War II, five events changed college basketball and allowed it to become a major spectator sport. In 1929, the rules committee reversed a decision that w

53、ould have outlawed dribbling and slowed the game considerably. Five years later, promoter Edward Ned Irish staged the first intersectional twin bill in Madison Square Garden in New York City and attracted more than 16,000 fans. He demonstrated the appeal of major college ball and made New York its c

54、enter. In December 1936, Hank Luisetti of Stanford revealed the virtues of the one-handed shot to an amazed Garden audience and became the first major collegiate star. Soon thereafter, Luisetti scored an incredible fifty points against Duquesne, thus ending the Easts devotion to the set shot and enc

55、ouraging a more open game. In consecutive years the center jump was eliminated after free throws and then after field goals, thus speeding up the game and allowing for more scoring. In 1938, Irish created the National Invitation Tournament (NIT) in the Garden to determine a national champion. Althou

56、gh postseason tournaments had occurred before, the NIT was the first with major colleges from different regions and proved to be a great financial success. The National Collegiate Athletic Association (NCAA) created its own postseason tournament in 1939 but did not rival the NIT in prestige for some

57、 time. The 1940s saw significant changes for college basketball. Players began using the jump shot after Kenny Sailors of Wyoming wowed the East with it in 1943. The behind-the-back dribble and pass also appeared, as did exceptional big men. Bob Kurland at Oklahoma A&M was almost seven feet tall and

58、 George Mikan at DePaul was six feet ten inches. While Kurland had perhaps the better college career and played in two Olympics, he chose not to play professional ball, whereas Mikan became the first dominant star in the pros. Their defensive play inspired the rule against goal tending (blocking a s

59、hot on its downward flight). Adolph Rupp, who played under Phog Allen, also coached the first of his many talented teams at Kentucky in that decade. However, in 1951, Rupp and six other coaches suffered through a point-shaving scandal that involved thirty-two players at seven colleges and seriously

60、injured college basketball, particularly in New York, where four of the seven schools were located. While the game survived, the NCAA moved its tournament away from Madison Square Garden to different cities each year and the NITs prestige began to decline. Professional basketball remained a disorgan