RS Aggarwal Solutions Class 9 Chapter 14 Statistics Solution

EXERCISE 14E

Question 1:
Mean marks of 7 students = 226
Sum of marks of seven students =(226×7)=1582
Marks obtained by 6 students = (340+180+260+56+275+307)
=1418
∴ Marks obtained by seventh student
= [(Sum of marks of 7 students)-(marks obtained by 6 students)]
=(1582-1418)=164
∴ Marks obtained by seventh student=164

Question 2:
Mean weight of 34 students = 46.5 kg
Total weight of 34 students =(34×46.5)kg =1581 kg
Mean weight of 34 students and the teacher =(46.5+0.5)kg=47kg (since 500 g = 0.5 kg)
∴ Total weight of 34 students and the teacher
=(47×35)kg =1645kg
∴ Weight of the teacher =(1645-1581)kg= 64kg

Question 3:
Mean weight of 36 students = 41 kg
Total weight of 36 students = 41x 36 kg = 1476kg
One student leaves the class mean is decreased by 200 g.
∴ New mean =(41-0.2)kg = 40.8 kg (since 200 g = 0.2 kg)
Total weight of 35 students = 40.8×35 kg = 1428 kg.
∴ the weight of the student who left =(1476-1428)kg =48 kg.

Question 4:
Mean weight of 39 students =40 kg
Total weight of 39 students = 40x 39) = 1560 kg
One student joins the class mean is decreased by 200 g.
∴ New mean =(40-0.2)kg = 39.8 kg (since 200 g = 0.2 kg)
Total weight of 40 students =(39.8×40)kg=1592 kg.
∴ the weight of new student
= Total weight of 40 students – Total weight of 39 students
= 1592-1560 = 32 kg

Question 5:
Mean salary of 20 workers =Rs.7650
Total salary of 20 workers =Rs(7650x 20)=Rs. 153000.
Now if managers salary is added mean becomes Rs. 8200
∴ Total salary of 20 workers + manager’s salary= Rs.(8200×21)
=Rs. 172200
∴ Manager’s salary per month
= Total salary of 20 workers and the Manager – Total salary of 20 workers
=Rs(172200-153000)
=Rs.19200

Question 6:
Mean monthly wage of 10 persons =Rs.9000
Total monthly wage of 10 persons=Rs(9000×10)
=Rs. 90000
New mean monthly wage

Question 7:
Mean consumption of petrol for the first 7 months=330 litres
Total consumption of petrol for the first 7 months=(330×7)liters=2310 litres
Mean consumption of petrol for the next five 5 months=270 litres
Total consumption of petrol for the next five 5 months=(270×5)=1350 litres
Total consumption of petrol in one year
=(2310+1350) litres
=3660 litres.
∴ Mean consumption of petrol = \(\frac { 3660 }{ 12 } \) = 305 litres per month

Question 8:
Mean of 15 numbers=18
Total sum of 15 numbers=(18×15)=270
Remaining numbers = 25 – 15 = 10
Mean of 10 numbers=13
Total sum of 10 numbers=(13x 10)=130
∴ Total sum of 25 numbers=(270+130)=400
∴ Mean of 25 numbers = \(\frac { 400 }{ 25 } \) = 16

Question 9:
Mean weight of 60 students = 52.75 kg
Sum of weight of 60 students = 60×52.75 kg
Mean weight of 25 students = 51
Sum of weight of 25 students = 25×51 kg
Remaining students = 60 – 25 = 35
Total weight of the remaining 35 students
= Sum of weight of 60 students – Sum of weight of 25 students
= (60×52.75 – 25×51)kg
=(3165-1275)=1890 kg
∴ Mean weight of remaining students = \(\frac { 1890 }{ 35 } \) = 54 kg

Question 10:
The increase in the average of 10 oarsmen = 1.5 kg
Total weight increased =(1.5×10) kg=15 kg
Since the man weighing 58 kg has been replaced,
Weight of the new man =(58+15)kg =73kg.

Question 11:
Mean of 8 numbers=35
∴ Total sum of 8 numbers = 35×8 = 280
Since One number is excluded, New mean = 35 – 3 = 32
∴ Total sum of 7 numbers = 32×7 = 224
the excluded number = Sum of 8 numbers – Sum of 7 numbers
= 280 – 224 = 56

Question 12:
Mean of 150 items = 60
Total Sum of 150 items = 150×60 = 9000
∴ Correct sum of items =[(sum of 150 items)-(sum of wrong items)+(sum of right items)]
= [9000 – (52 + 8) + (152 + 88)]
= [9000-(52+8)+(152+88)]
= 9180
∴ Correct mean = \(\frac { 9180 }{ 150 } \) = 61.2

Question 13:
Mean of 31 results=60
Total sum of 31 results = 31×60 = 1860
Mean of the first 16 results =16×58=928
Total sum of the first 16 results=16×58=928
Mean of the last 16 results=62
Total sum of the last 16 results=16×62=992
∴ The 16th result = 928 + 992 – 1860
= 1920 – 1860 = 60
∴ The 16th result = 60.

Question 14:
Mean of 11 numbers = 42
Total sum of 11 numbers = 42×11 = 462
Mean of the first 6 numbers = 37
Total sum of first 6 numbers = 37×6 = 222
Mean of the last 6 numbers = 46
Total sum of last 6 numbers = 6×46 = 276
∴ The 6th number= 276 + 222 – 462
= 498 – 462 = 36
∴ The 6th number = 36

Question 15:
Mean weight of 25 students = 52kg
Total weight of 25 students = 52×25 kg=1300 kg
Mean of the first 13 students = 48 kg
Total weight of the first 13 students = 48×13 kg = 624kg
Mean of the last 13 students = 55 kg
Total weight of the last 13 students = 55×13 kg = 715 kg
∴ The weight of 13th student
= Total weight of the first 13 students + Total weight of the last 13 students – Total weight of 25 students
= 624+715-1300 kg
= 39 kg.
Therefore, the weight of 13th student is 39 kg.

Question 16:
Mean score of 25 observations = 80
Total score of 25 observations = 80×25 = 2000
Mean score of 55 observations = 60
Total score of 55 observations = 60×55 =3300
Total no. of observations = 25+55 =80 observations
∴ Total score = 2000+3300 = 5300
∴ Mean score = \(\frac { 5300 }{ 80 } \) = 66.25

Question 17:
Average marks of 4 subjects = 50
Total marks of 4 subjects = 50×4 = 200
∴ 36 + 44 + 75 + x = 200
⇒ 155 + x = 200
⇒ x = 200 – 155 = 45
∴ The value of x = 45

Question 18:
Mean monthly salary of 75 workers = Rs. 5680
So, Total monthly salary of 75 workers = Rs. 5680×75 = Rs. 426000
Mean monthly salary of 25 workers = Rs. 5400
So, Total monthly salary of 25 workers = Rs. 5400×25 = Rs. 135000
Mean monthly salary of 30 workers = Rs. 5700
So, Total monthly salary of 30 workers = Rs. 5700×30 = Rs. 171000
Remaining workers = 75 – 55 = 20 workers
Total salary of remaining 20 workers
=Rs. [426000 – (135000 + 171000)]
= Rs. [426000 – 306000]
=Rs. 120000
∴ Mean salary of the remaining 20 workers= Rs. \(\frac { 120000 }{ 20 } \) = Rs. 6000

Question 19:
Let the distance of mark from the staring point be x km.
Then , time taken by the ship reaching the marks= \((\frac { x }{ 15 }) \) hours (since time = \(\frac { distance }{ speed } \)
Time taken by the ship reaching the starting point from the marks = \((\frac { x }{ 10 }) \) hours
Total time taken = \(\frac { x }{ 15 } \) + \(\frac { x }{ 10 } \) = \(\frac { x }{ 6 } \) hours
Total distance covered =x+x=2x km.
∴ average speed of whole journey = 2x ÷ \(\frac { x }{ 6 } \) = \(\frac { 2x\times 6 }{ x } \) = 12 km/hour

Question 20:
Total number of students = 50
Total number of girls = 50-40 = 10
Average weight of the class = 44 kg
Total weight of 50 students= 44x 50 kg = 2200kg
Average weight of 10 girls = 40 kg
Total weight of 10 girls = 40×10 kg = 400 kg
∴ Total weight of 40 boys = 2200-400 kg =1800 kg
∴ the average weight of the boys = \(\frac { 1800 }{ 40 } \) = 45 kg