Statistics Descriptive

Transcription

1 Statstcs Descrptve Ma aspects of descrbg a data set (a) Summarzazto ad descrpto of the data (1) Presetato of tables ad graphs (2) Scag the graphed data for ay uusual observatos wch seem to stck far out from the major mass of the data. (b) Computato of umercal measures for : (1) Represetatve value that dcates the ceter of the data. (2) The amout of spread or varato preset the data.

2 GENERAL FORMING FREQUENCY DISTRIBUTION Determe the largest ad smallest umbers the data ad thus fd rage = hghest score smallest score Determe a umber of class tervals. the umber of class tervals = 1 + (3,3) log Determe the wtdh class terval : (rage)/ (a umber of class tervals) Determe the umber of observatos fallg to class terval Example ( Pegatar Statstka, page 247 )

3 a. Sample Mea MEASURES OF CENTER (for data sets) The sample mea or average of a set of data x 1, x 2, x 3,.x s the sum of these measuremets dveded by. The mea s deoted by operatoally X, wth s expressed X 1 X

4 b. Meda The meda of a set of data x 1, x 2, x 3,.x s the mddle value whe the measuremets arragemet from smallest to largest. If s a odd umber, there s a uque mddle value ad t s the meda If s a eve umber, there are two mddle values ad the meda s defed as ther average

5 C. Mode The Mode of a set of data x 1, x 2, x 3,.x s that value whch occurs wth the greatest frequecy. Example : The set 2, 2, 3, 7, 9, 6, 5, 7 has mode 2. The set 3, 5, 7, 8, 10 has o mode The set 2, 3, 4, 5, 4, 6, 7, 6 has two mode, 4 ad 6 ad s called bmodal

6 EXAMPLE The brth weghts pouds of eght babes bor a hosptal o a certa day are 6,4 7,8 8,1 9,2 6,9 7,4 8,4 7,8 Fd the mea, the meda ad the mode of these data The grade of a studet o seve examatos were Fd the mea, the meda ad the mode of these data

7 MEASURES OF DISPERSION Mea Devato Mea devato (MD) from the data X 1, X 2,, X s gve by formula : Example : Fd the mea devato of the set of umbers 2, 3, 6, 8, 11 MD 1 X X

8 MEASURES OF VARIATION (for data sets) a. Varace s 2 of a set of data x 1, x 2, x 3,.x s defed as b. Stadard devato s defed as 1 ) ( X X S 1 ) ( 1 2 X X S

9 EXAMPLE The brth weghts pouds of eght babes bor a hosptal o a certa day are 6,4 7,8 8,1 9,2 6,9 7,4 8,4 7,8 Fd the mea devato, the varace ad the stadard devato of these data The grade of a studet o seve examatos were Fd the mea devato, the varace ad the stadard devato of these data

10 MEASURES OF CENTER (for grouped data) a. Mea If the frequecy dstrbuto has class tervals wth mdpots x 1, x 2 ad,, x correspodg frequeces f 1, f 2,., f, the X 1 f 1 f x 1 f x

11 b. Meda The formula for the meda s Me L me ( / c( 2) f F ) : exact lower lmt of the terval cotag the meda L me C : class terval F : sum of all frequecy below L me. f : frequecy of the terval cotag meda : umber of cases

12 The steps to fd the meda are Compute the comulatve frequecy Determe /2, oe half the umber of cases Fd the class terval whch the mddle case falls, ad determe the exact lmts of ths terval Iterpolate to fd a value o the scale above ad below whch oe half the total umer of cases falls. Ths s meda

13 c. Mode The formula for the mode s Mo L MO c( a a ) b : exact lower lmt of the terval cotag the mode : class terval : frequecy of the terval cotag mode - frequecy of the terval above L mo : frequecy of the terval cotag mode - frequecy of the terval below L mo L mo C a b

14 Example : from the data, fd the mea, the mode ad the meda Class terval frequecy

15 EXERCISES SOLVE THE EXERCISES FROM TEXT BOOK PENGANTAR STATISTIKA MATEMATIKA PAGE NO. 8, 14 ad 15

16 Quartles The formula for the mode s Q L K ((. ) / 4) { f F } c L q : exact lower lmt of the terval cotag the quartle C : class terval F : sum of all frequecy below L q f : frequecy of the terval cotag the quartle : umber of cases