2019年廣播電視大學《統(tǒng)計學原理》形成性作業(yè)（1-4）考核冊答案資料必考重點.doc

專業(yè)好文檔電大統(tǒng)計學原理形考作業(yè)一：(第一三章)一、判斷題1、 2、 3、 4、 5、 6、 7、 8、 9、 10、二、單項選擇題1、C 2、B 3、B 4、D 5、D 6、D 7、A 8、C 9、B三、多項選擇題 1、AD 2、BCE 3、ACE4、BCE 5、BCE 6、ACD四、簡答題1、標志是總體各單位所共同具有的某種屬性和特征，標志表現(xiàn)是標志特征在各單位的具體表現(xiàn)。標志分為品質(zhì)標志，如“性別”，“籍貫”；數(shù)量標志，如：年齡“，“工資”，相應的標志表現(xiàn)有品質(zhì)標志表現(xiàn)如“男”“杭州”；數(shù)量標志表現(xiàn)，如“20歲”，“2000元”。2、統(tǒng)計總體是根據(jù)一定的目的和要求所確定的研究事物的全體，它是由客觀存在的、具有某種共同性質(zhì)的許多個別事物構成的整體。樣本是從總體中抽取出來的用來代表總體的那部分單位，具有以下幾個特點：（1）樣本中的單位來自總體；（2）樣本是非唯一的；（3）樣本具有一定的代表性；（4）樣本具有客觀性。3、普查是專門組織的一次性全面調(diào)查。普查屬于不連續(xù)調(diào)查，調(diào)查內(nèi)容主要是反映國情國力方面的基本統(tǒng)計資料；而全面統(tǒng)計報表屬于連續(xù)調(diào)查，調(diào)查內(nèi)容主要是需要經(jīng)常掌握的各種統(tǒng)計資料。全面統(tǒng)計報表要經(jīng)常填報，因此報表內(nèi)容固定，調(diào)查項目較少；而普查是專門組織的一次性調(diào)查，在調(diào)查時可以包括更多的單位，分組更細、項目更多。因此，有些社會經(jīng)濟現(xiàn)象不可能也不需要進行經(jīng)常調(diào)查，但又需要掌握比較全面、詳細的資料時，就可通過普查來解決。普查花費的人力、物力和時間較多，不宜常組織，取得經(jīng)常性的統(tǒng)計資料還需要靠全面統(tǒng)計報表。4、調(diào)查對象與調(diào)查單位的關系是總體與個體的關系。調(diào)查對象是由調(diào)查目的決定的，是應搜集其資料的許多單位的總體；調(diào)查單位也就是總體單位，是調(diào)查對象所包含的具體單位。調(diào)查對象和調(diào)查單位概念不是固定不變的，隨著調(diào)查目的的不同二者可以互相變換。填報單位是負責上報調(diào)查資料的單位，填報單位與調(diào)查單位有時候一致，有時候不一致。例如：農(nóng)村耕地調(diào)查，調(diào)查對象是農(nóng)村所有的耕地，調(diào)查單位是每一塊耕地，填報單位是農(nóng)戶或農(nóng)業(yè)生產(chǎn)經(jīng)營單位。5、單項式分組就是以一個變量值為一組，組距式分組是以變量值變化的一個區(qū)間為一組。變量有離散變量和連續(xù)變量兩種，離散變量可一一列舉，而連續(xù)變量是連續(xù)不斷，相鄰兩組之間可作無限分割。所以，離散變量可作單項式分組和組據(jù)式分組，而連續(xù)變量則只能作組距式分組。在離散變量中，當變量值變動幅度較小時，采用單項式分組；當變量值變動幅度較大時，則采用組距式分組。6、基本步驟為：第一步：將原始資料按數(shù)值大小依次排列。第二步：確定變量的類型和分組方法（單項式分組或組距式分組）。第三步：確定組數(shù)和組距。當組數(shù)確定后，組距可計算得到：組距全距組數(shù)，全距=最大值最小值。第四步：確定組限（第一組的下限要小于或等于最小值，最后一組的上限要大于最大值）。第五步：匯總出各組的單位數(shù)，計算頻率，并編制分配數(shù)列。五、計算題1、等距分配數(shù)列可按照以下標準來編制 向上累計 向下累計工人數(shù) 企業(yè)數(shù) 比重 頻率 頻數(shù) 頻數(shù) 頻率200300 3 10 10 3 30 100300400 5 16.7 26.7 8 27 90400500 9 30 56.7 17 22 73.3500600 7 23.3 80 24 13 43.3600700 3 10 90 27 6 20700800 3 10 100 30 3 10不等距分配數(shù)列答案有多種，但基本的原則是要反映出一定的規(guī)律性。如：工人數(shù) 企業(yè)數(shù) 比重200250 1 3.4250400 7 23.3400600 16 53.3600700 3 10700800 3 102、分配數(shù)列如下：成績 人數(shù) 比重60以下 4 106070 6 157080 12 308090 15 37.590100 3 7.5合計 40 100分組標志為“成績”，為數(shù)量標志，該班考試成績?yōu)椤皟深^小，中間大”的鐘型分布。統(tǒng)計學原理形考作業(yè)二：（第四章）一、判斷題1、 2、 3、 4、 5、 6、 7、 二、單項選擇題1、A 2、C 3、D 4、B 5、C 6、D 7、B 8、B 9、D 10、C 11、D 12、D 三、多項選擇題 1、BE 2、ADE 3、ABC 4、DE 5、ADE 6、ADE 7、ABCDE 8、BDE 四、簡答題1、結構相對指標、比例相對指標和比較相對指標有什么不同的特點？請舉例說明。答：結構相對指標是以總體總量為比較標準，計算各組總量占總體總量的比重，來反映總體內(nèi)部組成情況的綜合指標。如：各種工人占全部工人的比重。比例相對指標是指總體不同部分數(shù)量對比的相對數(shù)，用以分析總體范圍內(nèi)各個局部之間比例關系和協(xié)調(diào)平衡狀況。如：輕重工業(yè)比例。比較相對指標是不同單位的同類指標對比而確定的相對數(shù)，用以說明同類現(xiàn)象在同一時期內(nèi)各單位發(fā)展的不平衡程度。如：甲地職工平均收入是乙地職工平均收入的1.3倍。2、強度相對指標與平均指標的區(qū)別是什么？答：主要區(qū)別：（1）其他各種相對指標都屬于同一總體的數(shù)量進行對比，而強度相對指標除此之外，也可以是兩種性質(zhì)不同的但又有聯(lián)系的屬于不同總體的總量指標之間的對比。（2）計算結果表現(xiàn)形式不同。其他相對指標用無名數(shù)表示，而強度相對指標主要是用有名數(shù)表示。（3）當計算強度相對指標的分子、分母的位置互換后，會產(chǎn)生正指標和逆指標，而其他相對指標不存在正、逆指標之分。3、如何理解權數(shù)的意義？在什么情況下，應用簡單算術平均數(shù)和加權算術平均數(shù)計算的結果是一致的？答：加權算術平均數(shù)中的權數(shù)，指的就是標志值出現(xiàn)的次數(shù)或各組次數(shù)占總次數(shù)的比重。在計算平均數(shù)時，由于出現(xiàn)次數(shù)多的標志值對平均數(shù)的形成影響大些，出現(xiàn)次數(shù)少的標志值對平均數(shù)的形成影響小些，因此就把次數(shù)稱為權數(shù)。在分組數(shù)列的條件下，當各組標志值出現(xiàn)的次數(shù)或各組次數(shù)所占比重均相等時，權數(shù)就失去了權衡輕重的作用，這時用加權算術平均數(shù)計算的結果與用簡單算術平均數(shù)的結果相同。4、什么是變異系數(shù)？變異系數(shù)的應用條件是什么？請寫出標準差變異系數(shù)的計算公式。答：變異系數(shù)是以相對數(shù)形式表示的變異指標。變異系數(shù)的應用條件是：為了對比分析不同水平的變量數(shù)列之間標志值的差異程度，就必須消除數(shù)列水平高低的影響，這時就要計算變異系數(shù)。5、請分別寫出結構相對指標、動態(tài)相對指標和強度相對指標的計算公式并舉例說明。答：結構相對指標，如：某門課程及格率為98。 動態(tài)相對指標，如：今年產(chǎn)量為去年的95。強度相對指標，如：人均國內(nèi)生產(chǎn)總值10000元/人。 6、請分別寫出簡單算術平均數(shù)、加權算術平均數(shù)、加權調(diào)和平均數(shù)的計算公式并分別說明其應用條件。答：簡單算術平均數(shù)：加權算術平均數(shù)： 加權調(diào)和平均數(shù)：簡單算術平均數(shù)適合于總體單位數(shù)比較少，資料沒有進行分組，而且標志值只出現(xiàn)一次的情況；加權算術平均數(shù)適合于總體單位數(shù)比較多，而且標志值不只一次出現(xiàn)，資料分組的情況；加權調(diào)和平均數(shù)適合缺少總體單位數(shù)的情況。各位電大的同學，插播一個小廣告，你們知道淘寶刷客嗎？就是幫淘寶賣家刷信譽的。商家給你紅包你去買它店里的東西，他的店就有信譽了，你也可以得到1-8快不等的傭金。想做的可以加我qq了解550168183，這個只是兼職，掙錢不多哈，時間是自由的。全職媽媽最好了。五、計算題1、解：甲產(chǎn)品的動態(tài)相對數(shù)： 乙產(chǎn)品的動態(tài)相對數(shù)： 丙產(chǎn)品的動態(tài)相對數(shù)：2002年計劃完成相對數(shù)：2、解：（1）按加工零件數(shù)分組 人數(shù) 比重2530 7 17.53035 8 20 3540 9 22.5 4045 10 254550 6 15合計 40 1003、解：4、解：平均勞動生產(chǎn)率5、解：（1）甲市場平均價格（2）平均單位產(chǎn)品成本所以甲市場的平均價格比較高。6、解： 統(tǒng)計學原理形考作業(yè)三：(第五七章)一、判斷題1、 2、 3、 4、 5、 6、 7、 8、 二、單項選擇題1、A 2、C 3、C 4、C 5、C 6、A 7、B 8、D 9、A 10、B11、B 12、D 三、多項選擇題 1、ABCD 2、ACD 3、BC 4、ABCE 5、BDE 6、AD 7、ABCD 8、BCDE 9、ABD 10、ACE四、簡答題1、什么是抽樣推斷？抽樣推斷都有哪幾方面的特點？答：抽樣推斷是在抽樣調(diào)查的基礎上，利用樣本的實際資料計算樣本指標，并據(jù)以推算總體相應數(shù)量特征的統(tǒng)計分析方法。特點：（1）是由部分推算整體的一種認識方法論；（2）建立在隨機取樣的基礎上；（3）運用概率估計的方法；（4）抽樣推斷的誤差可以事先計算并加以控制。2、什么是抽樣誤差？影響抽樣誤差大小的因素有哪些？答：抽樣誤差是指由于抽樣的偶然因素使樣本各單位的結構不足以代表總體各單位的機構，而引起抽樣指標和全及指標之間的絕對離差。影響抽樣誤差大小的因素有：總體各單位標志值的差異程度、樣本的單位數(shù)、抽樣方法和抽樣調(diào)查的組織形式。3、什么是參數(shù)和統(tǒng)計量？各有何特點？答：參數(shù)是一個全及指標，它反映了全及總體某種數(shù)量特征；統(tǒng)計量即樣本指標，它反映了樣本總體的數(shù)量特征。其特點是：全及指標是總體變量的函數(shù)，但作為參數(shù)其指標值是確定的、唯一的，是由總體各單位的標志值或標志屬性決定的；而統(tǒng)計量是樣本變量的函數(shù)，是總體參數(shù)的估計值，其數(shù)值由樣本各單位標志值或標志屬性決定，統(tǒng)計量本身也是隨機變量。4、什么是抽樣平均誤差和抽樣極限誤差？二者有何關系？答：抽樣平均誤差是反映抽樣誤差一般水平的指標；而抽樣極限誤差是反映抽樣誤差的最大范圍的指標，二者既有聯(lián)系又有區(qū)別。二者的聯(lián)系是：極限誤差是在抽樣平均誤差的基礎上計算得到的，即；二者的區(qū)別是：（1）二者涵義不同；（2）影響誤差大小的因素不同；（3）計算方法不同。5、請寫出相關系數(shù)的簡要公式，并說明相關系數(shù)的取值范圍及其判斷標準。答： 相關系數(shù)的簡要公式：（1）相關系數(shù)的數(shù)值范圍是在1和1之間，即（2）判斷標準：，；不相關，完全相關。6、擬合回歸方程yc=a+bx有什么前提條件？寫出參數(shù)a，b 的計算公式并解釋經(jīng)濟含義。答：擬合直線回歸方程的要求是：（1）兩變量之間確實存在線性相關關系；（2）兩變量相關的密切程度必須顯著；（3）找到合適的參數(shù)a、b，使所確定的回歸方程達到使實際的y值與對應的理論值的離差平方和為最小。 回歸方程中參數(shù)a 代表直線的起點值，在數(shù)學上稱為直線的縱軸截距，它表示x=0時y的常數(shù)項。參數(shù)b稱為回歸系數(shù)，表示自變量x增加一個單位時因變量y的平均增加值。回歸系數(shù)的正負號與相關系數(shù)是一致的，因此可以從回歸系數(shù)的正負號判斷兩變量相關的方向。六、計算題1、解：2、解：3、編制分配數(shù)列如下：成績 組中值 人數(shù) 比重60分以下 55 3 7.56070 65 6 157080 75 15 37.58090 85 12 3090100 95 4 10合計 40 1004、解：5、解：產(chǎn)量x 成本y xy 2 73 146 4 53293 72 216 9 51844 71 284 16 50413 73 219 9 53294 69 276 16 47615 68 340 25 4624合計 426 1481 79 30268 x=6代入方程6、解：設回歸方程表達式為當人均收入增加1元，銷售額平均增加0.92萬元x=14000代入7、解： 收入每增加1元，支出平均增加0.8元。統(tǒng)計學原理形考作業(yè)四：(第八九章)一、判斷題1、 2、 3、 4、 5、 6、 7、 二、單項選擇題1、A 2、A 3、B 4、C 5、B 6、D 7、A 8、B 9、C 10、D11、B 12、C 三、多項選擇題 1、ABE 2、CDE 3、ACD 4、AB 5、BCD 6、BC 7、ABCD 8、ABC 9、ABD 10、ABDE四、簡答題1、答：（1）綜合反映復雜現(xiàn)象總體數(shù)量上的變動狀況。它以相對數(shù)的形式，表明多種產(chǎn)品或商品的數(shù)量指標或質(zhì)量指標的綜合變動方向和程度。（2）分析現(xiàn)象總體變動中受各個因素變動的影響程度。包括現(xiàn)象總體總量指標和平均指標的變動受各個因素變動的影響程度分析。（3）利用連續(xù)編制的指數(shù)數(shù)列，對復雜現(xiàn)象總體長時間發(fā)展變化趨勢進行分析。2、答：數(shù)量指標綜合指數(shù) 質(zhì)量指標綜合指數(shù)一般情況下，編制數(shù)量指標綜合指數(shù)時，應以相應的基期的質(zhì)量指標為同度量因素；而編制質(zhì)量指標綜合指數(shù)時，應以相應的報告期的數(shù)量指標為同度量因素。3、答：平均指數(shù)要成為綜合指數(shù)的變形，必須在特定的權數(shù)的條件下。具體講，加權算術平均數(shù)指數(shù)要成為綜合指數(shù)的變形，必須在基期總值這個特定的權數(shù)條件下；加權調(diào)和平均數(shù)指數(shù)要成為綜合指數(shù)的變形，必須在報告期總值這個特定的權數(shù)條件下。列式證明如下：4、答：時期數(shù)列是指由反映現(xiàn)象在一段時期內(nèi)發(fā)展過程總量的時期指標構成的動態(tài)數(shù)列。時點數(shù)列是指由反映現(xiàn)象在某一瞬間總量的時點指標構成的動態(tài)數(shù)列。二者相比較有以下特點：（1）時期數(shù)列的各指標值具有連續(xù)統(tǒng)計的特點，而時點數(shù)列的各指標值不具有連續(xù)統(tǒng)計的特點。（2）時期數(shù)列各指標值具有可加性的特點，而時點數(shù)列的各指標值不能相加。（3）時期數(shù)列的各指標值的大小與所包括的時期長短有直接關系，而時點數(shù)列各指標值的大小與時間間隔長短無直接的關系。時期數(shù)列平均發(fā)展水平的計算公式：間斷時點數(shù)列平均發(fā)展水平計算公式：（間隔不等）（間隔相等）5、答：環(huán)比發(fā)展速度計算公式： 定基發(fā)展速度計算公式： 累積增長量計算公式： 逐期增長量計算公式：各期環(huán)比發(fā)展速度的連乘積等于定基發(fā)展速度：相鄰兩個時期的定基發(fā)展速度之商等于相應的環(huán)比發(fā)展速度： 逐期增長量之和等于累積增長量： 五、計算題1、解：（1）城鎮(zhèn)物價指數(shù)： 農(nóng)村物價指數(shù)：城鎮(zhèn)物價上漲13.45，農(nóng)村物價上漲16.39（2）產(chǎn)品成本指數(shù)：產(chǎn)品成本降低了72.7。2、解：（1）單位成本指數(shù)：（2）產(chǎn)量總指數(shù)：指數(shù)體系：3、解： 由于銷售量的變動對銷售額的影響額：350111.3238.69（萬元）4、（1）該商店上半年商品庫存額： （2）該商店下半年商品庫存額： （3）該商店全年商品庫存額： 5、解：6、解：年份199719981999200020012002城鎮(zhèn)居民可支配收入逐期增長量累積增長量定基發(fā)展速度（）環(huán)比發(fā)展速度（）定基增長速度（）環(huán)比增長速度（）5760.35425.1335.2335.294.1894.185.825.825854.0428.993.7101.63107.911.637.916280426519.7109.02107.289.027.286322.642.6562.3109.76100.689.760.686860537.41099.7119.09108.519.098.5平均增長量平均發(fā)展速度103.56平均增長速度平均發(fā)展速度13.567、解：（1）（2）14303233.21（億元）請您刪除一下內(nèi)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 television 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 Jordan, 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 court, 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 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. 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 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 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 ends 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 limited 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 friends 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 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 be 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; 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 previously 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 States, 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 basketball 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 construction 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 abided 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 State 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 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, 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 professional 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 WNBA 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, 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 league 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 contract 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 years. 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 Association, 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 ball 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 played 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 first 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 fouls 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 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, often 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 the 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 it 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 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 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. Wal