ML Aggarwal Solution Class 9 Chapter 20 Statistics Exercise 20.1

 Exercise 20.1

Question 1

Sol :

Given observations

8,6,10,18,1,3,4,4

∴Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{8+6+10+12+1+3+4+4}{8}=\frac{48}{8}$

=6


Question 2

Sol :

Number of peoples=5

Their replied hour=10,7,13,20,15

Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{10+7+13+20+15}{5}=\frac{65}{5}$
=13
∴13 hours were spent in their social work

Question 3

Sol :

Given six consecutive years

1620,2060,2540,3250,3500,3710

Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{1620+2060+2540+3250+3500+3710}{6}=\frac{16680}{6}$

=2780


Question 4

Sol :

The first twelve natural numbers are

1,2,3,4,5,6,7,8,9,10,11,12

Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{1+2+3+4+5+6+7+8+9+10+11+12}{12}=\frac{7}{12}$

=6.5


Question 5

Sol :

(i)

The first six prime numbers are 

2,3,5,7,11,13

Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{2+3+5+7+11+13}{6}=\frac{41}{6}$

=6.8333


(ii)

The first seven odd prime numbers are 

3,5,7,11,13,17,19

Mean$=\frac{\text { Sum of observations }}{\text { Total No of observations }}$

$=\frac{75}{7}=10 \frac{5}{7}$


Question 6

Sol :

(i)

Given works of a student are

81,72,90,90,85,86,70,93,71

Mean $=\frac{81+72+90+90+85+86+70+93+71}{9}=\frac{738}{9}$

=82


(ii)

The mean of age of three students is 15 years

Their ratio's are 4 : 5 : 6

Let Vijay's age is 4x

Rahul's age is 5x

Rakhi's age is 6x

$\frac{4 x+5 x+6 x}{3}=15$

$\frac{(4+5+6) x}{3}=15$

$\frac{15 x}{3}=15$

15 x=45

$x=\frac{45}{15}$

=3

Vijay age=4x

=4×3=12

Rahul age=5x

=5×3=15

Rakhi age=6x

=6×3=18

Vijay age=12 years

Rahul age=15 years

Rakhi age=18 years


Question 7

Sol :

(i)

The mean of 5 numbers is 20

One observation is included then mean is 6

Mean of 5 numbers =20×5=100

Let excluded number is "x"

The remaining numbers mean is 23

⇒5x-x=4x

=4×23=92

∴x=100-92=8

∴Excluded number is "8"


Question 8

Sol :

The mean of 25 observations is 27

One observation is included then the mean is 26 of observations

Then mean will remains same is "27"

∴Mean=27


Question 9

Sol :

Mean of 5 observations is 15=15×3=45

Mean of first 3 observations=14

⇒14×3=42

⇒42+d+e=75

⇒d+e=75-42=33

Mean of last 3 observations=17

⇒17×3=51

⇒a+b+51=75

⇒a+b=75-51=24


∴a+b+d+e+f=75

⇒24+33+f=75

⇒57+f=75

⇒f=75-157

=18

∴Third observation is 18


Question 10

Sol :

Mean of 8 variables=10.5

Given seven numbers are

3,15,7,19,2,17,8

Mean $=\frac{3+15+7+19+2+17+8+x}{8}$

⇒$10.5=\frac{71+x}{8}$

⇒10.5×8=71+x

⇒84=71+x

⇒x=84-71

⇒x=13


Question 11

Sol :

The mean weight of 8 students=45.5 kg

Mean weight of 8 students $=\frac{\text { sum of weights of } 8 \text { Students }}{8}$

$45.5=\frac{\text { sum of weights of } 8 \text { Students }}{8}$

Sum of weights of 8 students=45.5×8

=364 kg

Two weights of 41.7 and 53.3 kg are added

=364+41.7+53.3

Sum of weight of 10 students=459 kg

Mean $=\frac{\text { Sum of weights of } 10 \text { students }}{10}$

$=\frac{459}{10}$=45.9 kg


Question 12

Sol :

Mean of 9 observations=35

Mean of observations$=\frac{\text { Incoroect sum of } 9 \text { observations}}{9}$

35×9=Incorrect sum of 9 observations

Incorrect sum of 9 observations =315

One observation was detected as 81 was mi read as 18

=315-18+81

=378

Mean of 9 observations $=\frac{3.78}{9}$

=42


Question 13

Sol :

Given marks of 11 questions

7,3,4,1,5,8,2,2,5,7,6

These numbers were arranged in ascending order

1,2,2,3,4,5,5,6,7,7,8

∴Total number of observations=11

Median$=\frac{n+1}{8}$ th observation

$=\frac{11+1}{2}=\frac{12}{2}$

=6 th observation

∴Hence Median=5


Question 14

Sol :

Given numbers

2,3,4,3,0,5,1,1,3,2

Mean$=\frac{2+3+4+3+0+5+1+1+3+2}{10}=\frac{24}{10}$

=2.4

∴Mean=2.4

Median

The numbers were arranged in the form of ascending order

0,1,1,2,2,3,3,3,4,5

Median $=\frac{n+1}{2}=\frac{10+1}{2}=\frac{11}{2}$

=5.5 th observation

∴Median=2.5


Question 15

Sol :

Given numbers

24,30,28,17,22,36,30,19,32,18,20,24

Mean $=\frac{24+30+28+17+22+36+30+19+32+18+20+24}{12}=\frac{300}{12}$

=25

∴Mean=25

Median

The numbers are arranged in ascending order

17,18,19,20,22,24,24, 28,30,30,32,36

Median $=\frac{n+1}{2}=\frac{12+1}{2}=\frac{13}{2}$

=6.5 th observation

Median=25

Question 16

Sol :
Given numbers
41,39,52,48,54,62,46,52,40,96,42,40,98,60,52

Mean $=\frac{41+39+52+48+54+62+46+52+40+96+42+40+98+60+52}{15}$
$=\frac{822}{15}$
=54.8

∴Mean=54.8

Median
The numbers are arranged in the form of ascending order.
39,40,40,41,42,46,48,52,52,54,60,62,96,98

Median$=\frac{n+1}{2}=\frac{15+1}{2}=\frac{16}{2}$
=8
∴Median=811

Question 17

Sol :

The points scored by kabaddi team 

7,17,2,5,24,15,8,14,10,48,10,7,24,8,28,18

Mean $=\frac{7+17+2+5+27+15+8+14+10+48+10+7+24+8+28+18}{16}$

$=\frac{248}{16}$=15.5

Mean=15.5

Median

The points are arranged in the form of ascending order

2,5,7,7,8,8,10,10,14,15,17,18,24,27,28,48

Median$=\frac{n+1}{2}=\frac{16+1}{2}$

=8.5 th observation

Median=12


Question 18

Sol :

Given numbers

17,24,23,29,39,40, x, 50,51,54,59,67,91,93

Median$=\frac{\frac{n}{2} \text { th observation }+\left(\frac{n}{2}+1\right) \text { th } \text { observation }}{2}$

$47.5=\frac{7 \text { th observation }+8 \text { th obserration }}{2}$

$47.5=\frac{x+50}{2}$

95=x+50

x=95-50=45


Question 19

Sol :

Given numbers

3,6,7,10, x+x+4+19,20,25,28

Median $=\frac{\frac{n}{2} \text { th observation }+\left(\frac{n}{2}+1\right) \text { th observation }}{2}$

⇒$13=\frac{5th \text { ohservation }+6 \mathrm{th} \text { observation }}{2}$

⇒$13=\frac{x+x+4}{2}$

⇒13×2=2x+4

⇒26=2x+4

⇒2x=26-4

⇒2x=22

⇒$x=\frac{22}{2}$=11

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