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# Chapter 2.1 Stat 200

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This 5 page Class Notes was uploaded by Ayana Smith on Monday January 25, 2016. The Class Notes belongs to Stat 200 at Radford University taught by Dr. Kirtner in Spring 2015. Since its upload, it has received 21 views. For similar materials see Statistics 200 in Math at Radford University.

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Date Created: 01/25/16

Stat 200 21 Notes Frequency Distributions Defn A gl partitions data Into classes or Intervals and shows how many data values are in each class The classes are constructed so that each data value falls into exactly one class Stepsin Constructing a Frequency Table 1 First decide on how many Ol you want Use It s 5 e 15 usually and our problems will almost always tell us how many classes to choose 2 Find the l tg for the number of classes used Using the formula below and rounding up will give a good starting point for class width You will want to choose a width so that the classes formed present a clear representation of the data so use a sensible class width Class Width 2 let ate Eu Mott at deanquot 3 Find the C l l The Hi is the lowest data value than can fit in a Class 7 53 we r q ml3 it a w fquot l Era laquot The leakages t t t IS the highest data value that can fit in a class The leab g 7 is the difference between the lower class limit of first class the lower class limit ofthe next class Choose a starting value equal or a little less than the smallest data value After choosing the lower limit for the first class starting value add the class width to it to find the lower limit ofthe second class Continue this pattern until you have the desired number of lower class limits Next 5 the data into appropriate classes and find the frequency for each class The frequency of a class is the number of data values in it Notationi l h cuuuwcu e Ultith x WW 7 Compute the 7 for each class L Midpoint lbw CKrjicei imh t mpg Determine the bijiuti hdfht WE To find the Ql01 6 b ut ifihi ul add 05 to the upper class limit 0 To nd the lOWfJK laggt3 lCX hh r NC lCWLli subtract 05 from the lower class limit Find This refers to the proportion of all data values that fall into that class Relative frequency 2 E YECEWE39ZWCUI h fatm e ca cicite hem The total of all relative frequencies should equal 1 8 The Cumi mllih lf tildz l ifit tk LLt 77 quotif is the sum of the frequencies of a given class and all previous classes The cumulative frequency of the last class equals the sample size A r h39 LEM ill 7 Examgle How long does it take to finish the ll l mile Iditarod Dog Sled Rate from Anchorage 91 to Nome Alaska Finish time to the nearest hour for 57 dogsled teams are shown below m quot r 7 I 39 30 39 39339 00 g 0 quot H We Q1 Q7 39 E w 296 Q 299 293 2a Egg25613 u L r U J 7 7 r 7 r 39 estaifquot V r lb Sara 06 338 360 llama 9 RAW 237 296 X3 307 307 I 39 91 gag U U 5 j t t 3957quot u 3 use 7 3 F D 0 i in e o o is 299 303 77 304 305 288 29p 288 289 297 299 i i U x U quotm V J 5 23 a a u 7 3 D u m 7 a ir y 1 J 393 isq 309 34 337 is 291 235 233 535 groveaoeveaa U U a Find the class width Uses classes PE 7 1 gm 01 W mm 1 Vi narrates motto mullet ensuing u hvul t EM 39 er i 7 39 r 39U i mound 3 1 3 fr D W l lDWQy39 b Make a relative frequency table showing class limits class boundaries midpointsi U k lmt i frequencies and relative frequencies lower W igi l 2 33 nan 3 to LenW he st All l C39ilflll g Class Limits l Class l Tally Frequency Class l Cumulative Relative lower upper l Boundaries f Midpoint Frequency Frequency 1er tt i 3 j wquot i llquot 3 a e W 39m l r a n viii WET tau auo 2999 mi Ll 19 w s as tiei m r Hall 0 5 a limo Wlm 1m t MU 3595 loE 39 f g 2 33 7 95 media s Ell 33 lame ass lo 13 1 51 Ifls39i sitar 33 a sub sees w in 3 34 J E 099 l l 39 s l v c r 391 al tail J n 57 L F lquot Histograms and Relative Frequency Histograms Histograms and Relative Frequency Histograms provide effective visual displays of data organized into frequency tables In these graphs we use bars to represent each class where the width of the bar is the ggggs 7 E llglj j lln h gtg l39lgnvfg he height of the bar is the SE f39V c m nQu For relative frequency histograms the height ofthe bar is the Ml 7 of that class How to Make a Histogram or a RelativeaFrequency Histogram Histograms and relative frequency histograms provide effective visual displays of data organized into freq Uency tables In these graphs we use bars to represent each class 0 Horizontal axis classes These may be labeled with class limits class boundaries or class midpoints whichever makes most sense for your graph Vertical axis frequencies or relative frequencies Histograms represent numerical data and do Big have space between the bars 1 Make a fl i b i l i m 777 7 including relative frequencies with the desired number of cllasfses 2 Place ares llmradl iir l to Home mid burns or 0amp5 77f lll 7 7 7 on the horizontal axis and frequencies or relative frequencies on the vertical axis 3 For each class of the frequency table draw a bar whose h ig lii rlr extends between corresponding class boundaries Titleme le l thestrhrnl Owe l and the hm l CW 1 3 l 35 Example Using the data from the Idlitarod Dog Sled race from above construct a frequency histogram and a relative frequenc i istogram Hl l b y om 3 litlull l r p keg webe V w i i r ld m id 3900 r gl d Rout l Cli mr no Did we Will e mar 773 e Ml fl er 4 is 1 erg g r 26 qfs use a c c 39 iii J l 339quot g J l l g l 739 is Zf W W 1 Q g a U 7 7 f I l L l L 7 V 7 g r r39 39 jquot 1 quot r quot rag 6 Qm aeaws 2 1175 la6 55 a 39 frame rims one W ma a mommfi litit liiEi ll W11 Eli vileiih39 rb l g 7 Distribution Shapes If data has come from a random sample of population values the histogram constructed from the sample values should have a distribution shape that is reasonably similar to the population 1 Moundehaped svmmetricalz Both sides ofthe distribution are more or less mirror images There is a line of symmetry 2 Uniform or Rectangular Every value appears with nearly equal frequency lill 3 SkewedLeft or Slcewed Right One tail is stretched out longer than the other The direction of skewness is on the side of the longer tail skewed left or skewed right 4 Bimodal The two largest classes are separated by one or more classes Often implies Z expats lott iitir i SCH rm at f1 lineage two populations are sampled WI b in a data set are the data values that are very different from other measurements in a data set VU wank i

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