1、統計學原理復習（計算題） 1某單位40名職工業務考核成績分別為: 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單位規定：60分以下為不及格,6070分為及格,7080分為中,8090分為良,90100分為優。要求：(1)將參加考試的職工按考核成績分為不及格、及格、中、良、優五組并編制一張考核成績次數分配表；（2）指出分組標志及類型及采用的分組方法；（3）計算本單位職工業務考核平均成績（4）分析本單位職工

2、業務考核情況。解：（1）成 績職工人數頻率(%)60分以下60-7070-8080-9090-10036151247.51537.53010合 計40100 （2）分組標志為成績,其類型為數量標志；分組方法為：變量分組中的開放組距式分組,組限表示方法是重疊組限；（3）本單位職工業務考核平均成績（4）本單位的職工考核成績的分布呈兩頭小, 中間大的 正態分布的形態，說明大多數職工對業務知識的掌握達到了該單位的要求。22004年某月份甲、乙兩農貿市場農產品價格和成交量、成交額資料如下：品種價格（元/斤）甲市場成交額（萬元）乙市場成交量（萬斤）甲乙丙211合計5.5

3、4試問哪一個市場農產品的平均價格較高？并說明原因。解： 品種價格（元）X甲市場乙市場成交額成交量成交量成交額mm/xfxf甲乙丙1212合計5.5445.3解：先分別計算兩個市場的平均價格如下：甲市場平均價格（元/斤） 乙市場平均價格（元/斤） 說明：兩個市場銷售單價是相同的，銷售總量也是相同的，影響到兩個市場平均價格高低不同的原因就在于各種價格的農產品在兩個市場的成交量不同。 3某車間有甲、乙兩個生產組，甲組平均每個工人的日產量為36件，標準差為9.6件；乙組工人日產量資料如下：日產量（件）工人數（人）1525354515383413

4、要求：計算乙組平均每個工人的日產量和標準差； 比較甲、乙兩生產小組哪個組的日產量更有代表性？ 解：（1）（件） （件） （2）利用標準差系數進行判斷： 因為0.305 0.267故甲組工人的平均日產量更有代表性。 4某工廠有1500個工人，用簡單隨機重復抽樣的方法抽出50個工人作為樣本，調查其月平均產量水平，得每人平均產量560件，標準差32.45要求：（1）計算抽樣平均誤差（重復與不重復）； （2）以95%的概率（z=1.96）估計該廠工人的月平均產量的區間；（3）以同樣的概率估計該廠工人總產量的區間。 解： （1） 重復抽樣： 不重復抽樣： （2）抽樣極限誤差 = 1.964.59 =9件

5、月平均產量的區間： 下限: =560-9=551件 上限:=560+9=569件 （3）總產量的區間：（5511500 826500件； 5691500 853500件） 5采用簡單隨機重復抽樣的方法，在2000件產品中抽查200件，其中合格品190件.要求：（1）計算合格品率及其抽樣平均誤差（2）以95.45%的概率保證程度（z=2）對合格品率和合格品數量進行區間估計。（3）如果極限誤差為2.31%，則其概率保證程度是多少？ 解：(1)樣本合格率p = n1n = 190200 = 95% 抽樣平均誤差 = 1.54%(2)抽樣極限誤差p=zp = 21.54% = 3.08%下限:p=95

6、%-3.08% = 91.92%上限:p=95%+3.08% = 98.08% 則：總體合格品率區間：（91.92% 98.08%） 總體合格品數量區間（91.92%2000=1838件 98.08%2000=1962件） (3)當極限誤差為2.31%時，則概率保證程度為86.64% (z=) 6 某企業上半年產品產量與單位成本資料如下：月 份產量（千件）單位成本（元）123456234345737271736968要求：（）計算相關系數，說明兩個變量相關的密切程度。 （）配合回歸方程，指出產量每增加1000件時，單位成本平均變動多少？ （）假定產量為6000件時，單位成本為多少元？解：計算相

7、關系數時，兩個變量都是隨機變量，不須區分自變量和因變量。考慮到要配和合回歸方程，所以這里設產量為自變量（），單位成本為因變量（）月份產量（千件）單位成本（元）123456234345737271736968491691625532951845041532947614624146216284219276340合 計2142679302681481 （）計算相關系數：說明產量和單位成本之間存在高度負相關。（）配合回歸方程 =-1.82 =77.37 回歸方程為：.產量每增加1000件時，單位成本平均減少.元（）當產量為件時，即，代入回歸方程：.（元） 7根據企業產品銷售額(萬元)和銷售利潤率(%)

8、資料計算出如下數據: n=7 =1890 =31.1 2=535500 2=174.15 =9318 要求: (1) 確定以利潤率為因變量的直線回歸方程. (2)解釋式中回歸系數的經濟含義. (3)當銷售額為500萬元時,利潤率為多少? 解：（1）配合直線回歸方程： b= = =0.0365 a= =-5.41 則回歸直線方程為： yc=-5.41+0.0365x （2）回歸系數b的經濟意義：當銷售額每增加一萬元，銷售利潤率增加0.0365% （3）計算預測值： 當x=500萬元時 yc=-5.41+0.0365=12.8% 8 某商店兩種商品的銷售資料如下：商品單位銷售量單價（元）基期計算期

9、基期計算期甲乙件公斤50150601608121014要求：（1）計算兩種商品銷售額指數及銷售額變動的絕對額；（2）計算兩種商品銷售量總指數及由于銷售量變動影響銷售額的絕對額；（3）計算兩種商品銷售價格總指數及由于價格變動影響銷售額的絕對額。 解：（1）商品銷售額指數= 銷售額變動的絕對額：元 （2）兩種商品銷售量總指數= 銷售量變動影響銷售額的絕對額元 （3）商品銷售價格總指數= 價格變動影響銷售額的絕對額：元 9某商店兩種商品的銷售額和銷售價格的變化情況如下：商品單位銷售額（萬元）1996年比1995年銷售價格提高（%）1995年1996年甲乙米件12040130361012要求：(1)計

10、算兩種商品銷售價格總指數和由于價格變動對銷售額的影響絕對額。 (2)計算銷售量總指數,計算由于銷售量變動，消費者增加（減少）的支出金額。解：（1）商品銷售價格總指數= 由于價格變動對銷售額的影響絕對額：萬元 （2）)計算銷售量總指數:商品銷售價格總指數=而從資料和前面的計算中得知： 所以：商品銷售量總指數=，由于銷售量變動，消費者增加減少的支出金額: - 10某地區1984年平均人口數為150萬人，1995年人口變動情況如下：月份1369次年1月月初人數102185190192184計算：（1）1995年平均人口數;（2）1984-1995年該地區人口的平均增長速度.解：（1）1995年平均人

11、口數=181.38萬人（2）1984-1995年該地區人口的平均增長速度： 11某地區19951999年糧食產量資料如下：年份1995年1996年1997年1998年1999年糧食產量（萬斤）434472516584618要求：（1）計算各年的逐期增長量、累積增長量、環比發展速度、定基發展速度；（2）計算1995年-1999年該地區糧食產量的年平均增長量和糧食產量的年平均發展速度；（3）如果從1999年以后該地區的糧食產量按8%的增長速度發展，2005年該地區的糧食產量將達到什么水平？ 解：（1）年 份1995年1996年1997年1998年1999年糧食產量（萬斤） 環比發展速度 定基發展速

12、度逐期增長量累積增長量434-4721087610876383851610932118894482584113181345668150618105821424034184平均增長量=（萬斤）（萬斤） （2）平均發展速度（3）=980.69（萬斤） 12年 份1995年1996年1997年1998年1999年糧食產量（萬斤） 環比發展速度 逐期增長量 434- 10876 44 68 10582 要求：（1）計算各年的逐期增長量、累積增長量、環比發展速度、定基發展速度；（2）計算1995年-1999年該地區糧食產量的年平均增長量和糧食產量的年平均發展速度；（3）如果從1999年以后該地區的糧食產

13、量按8%的增長速度發展，2005年該地區的糧食產量將達到什么水平？ （做法見上題）請您刪除一下內容，O(_)O謝謝！2016年中央電大期末復習考試小抄大全，電大期末考試必備小抄，電大考試必過小抄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