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=−6−2−1+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=40−27⇒y+x=13
∴y=13−x
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+x5⇒80=312+x5⇒400=312+x∴x=400−312=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 =∑fx∑f=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 0−88−1616−2424−3232−4040−48 Students 53101642
Sol:
marks 8xfx0−854208−163123616−24102020024−32162844832−4043614440−4824288 total 40936
Meam =εfxεt=93640=23.4 Marks
Question 9
Fill the mean of the following data:
(a)
Marks 10−1415−1920−2425−2930−34 Student 461253
(b)
Class 0−1011−2021−3031−4041−50 frequency 34256
Sol: (a)
Marks Student ( f) xf×x10−144124815−1961710220−24122226425−2952713530−3433296 Tolel 30645
Mean=εfxεf= 578.520
=28.925
Question 10
In a class of 60 boys the marks obtained in a monthly test were as under :
Marks 10−2020−3030−4040−5050−60 Students 1025120005
Find the mean marks of class
Sol: Marks students (f) xf×x10−20101515020−30252562530−40123542040−500836056−600555275601830183
Mean =∑fx∑f= 183060=1836=30.5
Question 11
(i) Direct method and (ii) short cut method
Class 5−1010−1515−2020−2525−3030−3535−4040−4545−50 frequency 10641284213
Sol: (image to be added)
(i) Direct method
Mean =∑⋅d∑f=110050=22
(ii) Short cut method
Mean = A+ =\frac{\sum \cdot d}{\sum f}
=27.5+−27550
=27.5−5.5=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 kg0−22−44−66−618−1010−1212−7414−1616−18 No.0fectss 41417201013121010
Calculate the mean correct to first place of decimal
Sol:
Amount of milk cows (f)xf×x0−24142−4143424−6175856−82071408−101099010−12131114312−14121315614−16101515016−181017170 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 70−89,90−109 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=139.5−1465=139.5−29.2
=110.3gm
Question 14
The following table given the weekly wages of workers in a factory
Weekly Wages (Rs) 50−5555−6060−6565−7070−7575−8080−8585−90 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:
50−55552.5−15−7555−602057.5−10−20060−651062.5−5−5065−701067.5=A0070−75972.55.6575−80677.5101580−851282.51516085−90897.520120 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×x0−105773510−2015191210020−3025321332530−4035421035040−5045508360501250
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=27.5−8015=27.5−163=27.5−5.3=22.2
Question 17
Find the missing frequency in the following
class 4−88−1212−1616−2020−2424−2828−3232−3636−40 Frequency 11131614−91764
Sol: Suppose that the missing frequency is p
Class frequency fxf×x4−8116668−12131013012−16161422416−20141825220+24p2222p24−2892623422−32173051032−3663420436−40438152 Toral 90+pεfx=1772+22p
mean =εfxεt
19.92=1772+22p90+p⇒1772+22p=1792.8+19.92p
⇒22p−19.92p=1792.8−17722.08p=20.8⇒p=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 0−1010−2020−3030−4040−50 No.of students) 252087
Sol:
Marks no of students xf×x0−10251010−205157520−30202550030−4083528040−50745315εf=42εx=1180
Mean =εfxεf=118042=28.095=28.1
Question 19
Following table gives marks scored by student in an examination
4 Marks 0−55−1010−1515−2020−2525−3030−3535−40 No.of 3T152416852 Student $
Ans:
Marks No of student(f)xAd=x−Af×d0−532.5−15−455−1077.5−10−7010−151512.5−5−7515−202417.517.50020−251622.558025−30827.5108030−35532.5157535−40237.52040total∑f=80εfd=85
Mean =A+εtdεf=17.5+8580=17.5+1.06=18.56=18.56
No comments:
Post a Comment