f f... f 1 n n (ii) Median : It is the value of the middle-most observation(s).

Transcription

1 CHAPTER STATISTICS Pots to Remember :. Facts or fgures, collected wth a defte pupose, are called Data.. Statstcs s the area of study dealg wth the collecto, presetato, aalyss ad terpretato of data.. The data collected by the vestgator hmself wth a defte objectve md are kow as Prmary data.. The data collected by somoe else, other tha the vestgator, are kow as Secodary data.. Ay character whch s capable of takg reversal dfferet values s called a varable.. Each group to whch the raw data are codesed s kow as class-terval. Each class s bouded by two fgures kow as ts lmts. The fgure o the left s lower lmt ad fgure o the rght s upper lmt.. The dfferece betwee true upper lmt ad true lower lmt of a class s kow as ts class-sze.. Md-value of a class (or class mark) = upper lmt lower lmt. Class sze s the dfferece betwee ay two successve class marks (md-values).. The dfferece betwee the maxmum value ad the mmum value of the varable s kow as Rage.. The cout of umber of observatos a partcular class s kow as ts Frequecy.. The data ca be preseted graphcally the form of bar graphs, hstograms ad frequecy polygos.. The three measures of cetral tedecy for a ugrouped data are : () Mea : It s foud by addg all the values of the observatos ad dvdg t by the total umber of observatos. It s deoted by x. x So, x x... x x For a ugrouped frequecy dstrbuto,. fx f x... fx x f f... f fx f () Meda : It s the value of the mddle-most observato(s). If s a odd umber, the meda = value of the MATHEMATICS IX STATISTICS th observato. ad, f s a eve umber, the meda = mea of the values of ad () Mode : The mode s the most frequetly occurrg observato. Emprcal formula for calculatg mode s gve by, Mode = (Meda) (Mea) th th observatos.

2 ILLUSTRATIVE EXAMPLES Example. The relatve humdty ( %) of a certa cty for a moth of 0 days was as follows : () Costruct a grouped frequecy dstrbuto table wth classes -, - etc. () Whch moth or seaso do you thk ths data s about? () What s the rage of ths data? NCERT Soluto. () Frequecy dstrbuto table Relatve humdty ( %) () Moth-Jue or seaso-mosoo () Rage Tally Marks Frequecy STATISTICS MATHEMATICS IX = Maxmum observato mmum observato =.. =. Example. The value of upto 0 decmal places s gve below : Soluto..0 () Lst the dgts from 0 to ad make a frequecy dstrbuto of the dgts after the decmal pot. () What are the most ad the least frequecy occurrg dgts? NCERT () Frequecy dstrbuto table Dgt 0 Tally Marks Frequecy () Most frequecy occurg dgts are ad, ad least occurrg dgt s

3 Example. The followg table gves the lfe tmes of 00 eo lamps: Soluto. Example. Lfe tme ( hours) lamps () Represet the gve formato wth the help of a hstogram. () How may lamps have a lfe tme of more tha 00 hours? () () lamps havg lfe tme more tha 00 hours = + + = 0 NCERT The followg two tables gve the dstrbuto of studets of two sectos accordg to the marks obtaed by them : Secto A Secto B Marks Frequecy Marks Frequecy Represet the marks of the studets of both the sectos o the same graph by frequecy polygo. MATHEMATICS IX STATISTICS

4 Soluto. Requred frquecy polygo s as follows : Example. Draw hstogram of the weekly pocket expeses of studets of a school gve below : Soluto. Weekly pocket expeses ( Rs. ) studets Here, we observe that class tervals are uequal, so we wll frst adjust the frequeces of each class terval. Here, the mmum class sze s. We kow, Adjusted frequecy of a class terval Mmum class sze frequecy of the class classsze The adjusted frequecy of each class terval s gve below : Weekly pocket expeses Frequecy STATISTICS MATHEMATICS IX Adjusted frequecy

5 So, requred hstogram s gve below. Example. I a mathematcs test gve to studets, the followg marks (out of 0) are recorded :,,,,,,, 0,,,, 0,,, 0. Fd the mea, meda ad mode of the above marks. Soluto. () Mea ( x) x () Arragg the data the ascedg order : here,, 0, 0,,,,,,,,, 0,,, =, whch s odd. meda = value of th th observato observato = th observato = () Sce, occurs most frequetly.e. tmes, so mode s. MATHEMATICS IX STATISTICS

6 Example. Fd the mea salary of 0 workers of a factory from the followg table: NCERT Soluto. Example. Salary( Rs. ) x f x Mea ( x) f Salary ( Rs) workers f 0 STATISTICS MATHEMATICS IX No.of workers f 0000 Rs f x As f x 0000 The mea of umbers s. If oe umber s excluded, ther mea s. Fd the excluded umber. Soluto. Here, =, x. x Now, x x 0 So, total of umbers s 0. Let the excluded umber be a. The, total of umbers s 0 a. 0 a Mea of umbers 0 a 0 a = a = the excluded umber s. As. ( Gve, ew mea = )

7 Example. The meda of the observatos,,,, x +, x +, 0,,, arraged ascedg order s. Fd x. Soluto. Here, =. Sce s eve : th th observato observato Meda th observato th observato ( x ) ( x ) x x x = As. Example. Fd the mode for the followg data :,,,,,,,,,,,. Soluto. Arragg the gve data ascedg order:,,,,,,,,,,, Sce, occurs maxmum umber of tmes ( tmes), s the requred mode. PRACTICE EXERCISE. Costruct a frequecy table for the followg ages ( years) of 0 studets usg equal class tervals, oe of them beg -, where s ot cluded.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. The electrcty blls ( Rs.) of 0 houses a localty are gve below :,, 0,, 0,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 0,,, Costruct a grouped frequecy table.. For the followg data of weekly wages ( Rs.) receved by 0 workers a factory, costruct a grouped frequecy dstrbuto table.,, 0, 00, 0,,,,,,,,, 0,, 0, 0,, 0,,,, 0,,,, 0,,, 00. Costruct a frequecy table, wth equal class-tervals from the followg data o the weekly wages ( Rs.) of labourers workg a factory, takg oe of the class-tervals as 0-00 (00 ot cluded). 0,,,, 0,,, 0, 0, 0,,, 00, 0,,,, 0,,,, 0,,, 0. Gve below are two cumulatve frequecy dstrbuto tables. Form a frequecy dstrbuto table for each of these. () () Ages ( years ) Below Below 0 Below 0 Below 0 Below 0 Below 0 persos 0 0 Marks obtaed More tha More tha 0 More tha 0 More tha 0 More tha 0 More tha 0 Studets MATHEMATICS IX STATISTICS 0 0

8 . O a certa day, the temperature a cty was recorded as uder : Tme a.m. a.m. a.m. p.m. p.m. Temperature ( C) 0 Draw a bar graph to represet the above data.. Read the bar graph gve below ad aswer the questos gve below : () What formato s gve by the bar graph? () I whch year was the producto maxmum? () After whch year was there a sudde fall the producto? (v) Fd the rato betwee the maxmum ad mmum producto durg the gve perod.. The table gve below shows the umber of blds a vllage : Age group blds 0 Draw a hstogram to represet the above data.. The followg table shows the average daly eargs of 0 geeral stores a market, durg a certa week. Daly earg ( Rs. ) stores STATISTICS MATHEMATICS IX 0

9 Draw a hstogram to represet the above data.. The followg table gves the heghts of 0 studets of a class. Draw a frequecy polygo to represet ths. Heght ( cm) Studets I a study of dabetc patets a vllage, the followg observatos were oted. Represet the gve data by a frequecy polygo Age ( Years) Patets. Draw a hstogram ad a frequecy polygo o the same graph to represet the followg data : Weght ( cm) Persos Draw a hstogram to represet the followg frequecy dstrbuto. Class Iterval Frequecy MATHEMATICS IX STATISTICS

10 . Draw a hstogram for the marks of studets gve below : Marks Studets. The rus scored by two teams A ad B o the frst 0 balls a crcket match are gve below : Number of balls STATISTICS MATHEMATICS IX Team A 0 0 Team B Represet the data of both the teams o the same graph wth the help of frequecy polygos.. Fd the mea for each of the followg sets of umbers : (),,,,, 0, ().,.,.,.,.,. (),,,,, (v),,,,. Calculate the mea ( x ) for each of the followg dstrbuto : () x f () x f. The followg table shows the umber of accdets met by 0 workers a factory durg a moth : accdets workers 0 Fd the average umber of accdets per workers.. The marks obtaed out of 0 by 0 studets a test are gve below : Marks Studets 0 Calculate the average marks. 0. If the mea of the followg data s., fd the value of p. f 0 0 x p 0 0 0

11 . The average of heght of 0 boys out of a class of 0, s 0 cm. If the average heght of the remag boys s cm, fd the average heght of the whole class.. The average of sx umbers s 0. If the average of frst four s ad that of last three s, fd the fourth umber.. The mea of 0 observatos was calculated as 0. It was foud later o that oe of the observatos was msread as stead of. Fd the corrected mea.. The mea of umbers s. If s subtracted from every umber, what wll be the ew mea?. If x s the mea of observatos x, x,..., x, the prove that ( x x) 0.e. the algebrac sum of devatos from mea s zero.. Fd the meda of followg data : (),,,,,,,, (),,,,,,,. The umbers,,,, x, x +,,,, 0 are arraged ascedg order. If ther meda s, fd the value of x.. Fd the meda of the followg observatos :,,,,,,,, 0,,. If s replaced by ad by the above data, fd the ew meda.. Fd out the mode of the followg data : (),,,,,,,,, ().,.,.,.,.,.,.,.,. 0. Gve below s the umber of pars of shoes of dfferet szes sold a day by the ower of the shop. What s the modal shoe sze? Sze of shoe pars sold MATHEMATICS IX STATISTICS PRACTICE TEST MM : Tme : hour Geeral Istructos : Each questo carry marks.. Three cos were tossed 0 tmes smultaeously. Each tme the umber of heads occurg was oted dow as follows: Prepare a frequecy dstrbuto table for ths data.. A radom survey of the umber of chldre of varous age groups playg a park was foud as follows: Age ( years ) chldre Draw a hstogram to represet the data above

12 . Fd mea ( x ) for the followg dstrbuto: x f 0 0. The followg observatos have bee arraged ascedg order. If the meda of the data s, fd the value of x.,,, 0, x, x +,,,,. The marks obtaed by 0 studets a test are gve. Fd the modal marks () No.of Marks Class Frequecy Class Frequecy studets Weekly Wages ( Rs.) workers Weekly Wages () ( Rs.) workers Age ( year) persos Studets 0 ANSWERS OF PRACTICE EXERCISE Marks obtaed STATISTICS MATHEMATICS IX

13 .. () The gve bar graph shows the producto ( mllo toes) of food gras durg the perod from 000 to 00. () 00 () 000 (v) :.... MATHEMATICS IX STATISTICS

14 STATISTICS MATHEMATICS IX

15 . (). (). (). (v). ().0 ()..... (approx) cm..... () () 0...,. () () ANSWERS OF PRACTICE TEST MATHEMATICS IX STATISTICS