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S Chand Class 10 CHAPTER 18 Arithmetic Mean, Median, Mode and Quartiles Exercise 18 A

 Exercise 18 A 

Question 1

Find the number half way between 0.2 and 0.02,

Ans: Halfway number  (average)0.2+0.022=0.222=0.11

Question 2
Find the mean of the following sets of number
(i) 4,5,7,8 (ii) 3,5,0,2,8 (iii) 2.5,2.4,3.5,2.8,2.9,3.5 and 3.6 (iv) 6,2,1,0,1,2,5,9
(v) first five prime number  (vi) First eight even natural number (ix) x, x+1, x+2,x+3,x+4,x+5 and x+6
 
Sol: (i) here n= 4
Mean =4+5+7+84=244=6

(ii) n=5
 Mean =3+5+0+2π85=185=3.6

(iii) n=7
Mean =2.5+2.4+3.5+2.8+2.9+3.3+3.67
=21.07=3.0

(iv) n=8
 Mean =6+(2)+(1)+0+1+2+5+98=621+0+1+2+5+98=88=1

(v) First 5 prime number are 2,3,,4,711
Mean = 2+3+5+7+115=285=5.6

(vi) First 8 even natural number are 2,3,6,8,10,12,14 and 16
Mean = 2+4+6+8+10+12+14+168=728=9

(vii) all factors of 30 are 1,2,3,5,6,10,15,30
Here n- 8
Mean = 1+2+3+5+6+10+15+308=728=9

(viii) First 5 multiple of 8[ are 8,16,24,32,40 here n = 5
Mean =8+16+24+32+405=1205=24

(ix) Here n=7
 Mean =x+x+1+x+2+x+3+x+4+x+5+x+67=7x+217=7(x+3)7=x+3

Question 3
The mean of the number 6,y,4 , x ,14 is 8 express y in terms of x 
Sol: Mean =6+y+7+x+145
8=x+y+275
40=x+y+27
y+x=4027y+x=13
y=13x

Question 4
Nisha secured 73,86 ,78 and 75 marks in four tests what is the least number of points she should secure in her test if she has to have an average of 80.

Sol: Number of total tests = 5 
Average of 5 tests -80 
Suppose that the next test secure is x than 
 Mean =73+86+78+75+x580=312+x5400=312+xx=400312=88

Question 5
A class of 10 students was given a test in math . The marks out of 50 secured by the students were as follows  31,36,27,38,45,39,32,29,41,38. find the mean Score

Sol: Here n= 10 and scores are 31,36,27,38,45,39,32,29,41,38
 Mean =31+36+27+38+45+39+32+29+41+3810=35610=35.6

Question 6
Find the mean of the following frequency distribution: 
 (a)  Weight 3031323334 Noogslucenk 8101589

(b) 
 Marks 2025303540 Student 5101285

(c)
 x2578y2463

(d)
 x0.10.20.30.40.50.6y306020401050

Sol: (a)
 Weight  No of students f×x30824031103103215480338264349306 Total 501600
 Mean =fxf=160050=32 kg

(b)
 Marks (x) Students (t)f×x20510025102503012360358280405200 total401190
 Mean =εfxεf=119040=1194=29.75

(c) 
 xff×x224542076428324 total 1590
 Mean =εfxεf=9015=6

(d)
xff×x0.13030.260120.32060440160.51050.65030 Tolat 21072

 Mean =εfxεf=72210=1235=0.34.

Question 7
Fill in the blanks 
While calculating the mean of a the grouped data. We make the assumption that frequency is any class is entered at its.......

Sol: Mean of grouped data in any class is called its class mark 

Question 8
The frequency distribution of marks obtained by 40 students of a class is as under calculate the arithmetic mean 
 Marks 088161624243232404048 Students 53101642

Sol:  
 marks 8xfx0854208163123616241020200243216284483240436144404824288 total 40936
 Meam =εfxεt=93640=23.4 Marks 

Question 9

Fill the mean of the following data: 
(a)
 Marks 10141519202425293034 Student 461253

(b) 
 Class 0101120213031404150 frequency 34256

Sol: (a) 
 Marks  Student ( f) xf×x1014412481519617102202412222642529527135303433296 Tolel 30645

Mean=εfxεf578.520
=28.925

Question 10
In a class of 60 boys the marks obtained in a monthly test were as under : 
 Marks 10202030304040505060 Students 1025120005
Find the mean marks of class 

Sol:  Marks  students (f) xf×x10201015150203025256253040123542040500836056600555275601830183
Mean =fxf183060=1836=30.5 

Question 11
(i) Direct method and (ii) short cut method 
 Class 51010151520202525303035354040454550 frequency 10641284213

Sol: (image to be added)

(i) Direct method
 Mean =df=110050=22

(ii) Short cut method 
Mean = A+ =\frac{\sum \cdot d}{\sum f}
=27.5+27550
=27.55.5=22

Question 12
The following table givens the classification of 100 cows of a dairy form . According to the amount of milk given by each in a dairy 
 Amount of milk in kgno. of cows1 kg0224466618101012127414161618 No.0fectss 41417201013121010

Calculate the mean correct to first place of decimal 

Sol: 
 Amount of milk cows (f)xf×x0241424143424617585682071408101099010121311143121412131561416101515016181017170 Jotel 150980
Mean =εfxεf=980110=8.9=8.9

Question 13
The weight of 50 apples picked out at random from a are given below:-82,118,80,110,104,84,106,107,76,82,109,107,115 93,187,95,123,125,111,92,86,70,126,70,130,129,139,119,115,128,100,186
84,99,113,204,111,141,136,123,90,115,98,110,78,90,107,81,131,75.
(i) What the range of weights 
(ii) Form a frequency distribution with class- interval 7089,90109 and So on 
(iii) Use your frequency distribution to calculate the mean 

Sol: (i) Maximum weight = 204g
Minimum weight = 70g 
Range= 204-70=134gm

(ii)Frequency distribution:-
(IMAGE TO BE ADDED)

(iii)  Mean =A+εfdεf=139.5+(1460)50=139.51465=139.529.2
=110.3gm

Question 14
The following table given the weekly wages of workers in a factory 
 Weekly Wages (Rs) 50555560606565707075758080858590 No. of worker520101096128

Calculate (i) The mean(ii) The number of workers getting weekly wages below Rs 80 and (iii) the number of workers getting Rs 65 and more but tea than 85 as weekly wages 

Sol:
5055552.5157555602057.51020060651062.555065701067.5=A007075972.55.657580677.5101580851282.5151608590897.520120 Total 80120

(i)  Mean =A+εfdεt=67.5+12080=67.5+1.5=69.0

(ii) Number of workers getting wages below 80 = 60
(iii) Number of workers getting more than Rs 65 but less then Rs 85 = 10+9+6+12=37

Question 15
Find the mean of following data
(IMAGE TO BE ADDED)

Sol:  
 Marks obtained  Class-mark No  No of workers ff×x01057735102015191210020302532133253040354210350405045508360501250
Mean =εfxεf=125050=1255=25

Question 16
The following table into the form of an ordinary frequency distribution and determine the value of mean 
(IMAGE TO BE ADDED)

Sol: 
(IMAGE TO BE ADDED)
 Mean =A+εffεf.=27.5+800150=27.58015=27.5163=27.55.3=22.2

Question 17
Find the missing frequency in the following 
 class 488121216162020242428283232363640 Frequency 1113161491764

Sol: Suppose that the missing frequency is p

 Class  frequency fxf×x48116668121310130121616142241620141825220+24p2222p24289262342232173051032366342043640438152 Toral 90+pεfx=1772+22p

mean =εfxεt
19.92=1772+22p90+p1772+22p=1792.8+19.92p

22p19.92p=1792.817722.08p=20.8p=20.82.08=10

Question 18
Calculate the A.M correct to one decimal place for the following frequency distribution of marks obtained in an arithmetic test
 Marks 0101020203030404050 No.of students)  252087

Sol: 
 Marks  no of students xf×x01025101020515752030202550030408352804050745315εf=42εx=1180
Mean =εfxεf=118042=28.095=28.1

Question 19
Following table gives marks scored by student in an examination 
4 Marks 05510101515202025253030353540 No.of 3T152416852 Student $

Ans: 
 Marks  No of student(f)xAd=xAf×d0532.5154551077.5107010151512.557515202417.517.50020251622.55802530827.510803035532.515753540237.52040totalf=80εfd=85
 Mean =A+εtdεf=17.5+8580=17.5+1.06=18.56=18.56


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