Question

Chapter : Statistics

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Answer 1

Answer:

1) 19

Step-by-step explanation:

$mean = \frac{sum \: of \: observations}{total \: number \: of \: observations}$

$\frac{6 + 7 + x + 8 + y + 14}{6 } = 9$

Transposing 6 to RHS and adding the terms, we get,

$35 + x + y = 9 \times 6$

$35 + x + y = 54$

Transposing 35 to RHS we get

$x + y = 54 - 35 = 19$

2)

$mean \: of \: first \: n \: natural \: numbers = \frac{sum \: of \: first \: n \: natural \: numbers}{total \: numbers}$

Answer 2

Answer no 1:

x +y =19.

Explanation:

It's simple.

$\frac{6 + 7 + 8 + 14 + x + y}{6} = 9$

=>6+7+8+14 +x+y =54

Hence,

=> x + y = 19

Answer no 2:

63.

Explanation:

Sum of (n)natural numbers:

$n.\dfrac{(n + 1)}{2}$

Mean of the (n) natural numbers:

$n.\dfrac{n + 1}{2n} = 32$

So,

$32 \times 2 = 63$

Hence,

n = 63.

Answer no 3:

46.

Explanation:

Given that,

Mode of the data = 43

Data are 64, 60, 48, x, 43 , 48, 43, 34

Values are:

34 | 43 | 48 | 60 | 64 | x |

Frequency:

1| 2 | 2 | 1 | 1 | 1 |

Also given that,

Mode of the data is 43,

Hence,

It is the value of maximum frequency.

Therefore,

x+ 3 = 43 + 3 = 46

Hence,

The value of x+3 = 46.

Answer no 4:

x = 25.

Explanation:

24 , 25, 26 , x + 2, x + 3, 30, 31, 34 n = 18

(These all are even numbers)

Median average of nth/2 form and

nth/2+ 1 form. 4/2 = 4th form =x+2

n/2 +1 = 4+1 form and,

5th form = x+3

Average =

$\dfrac{(x + 2)(x + 3)}{2} = 27.5$

=>2x+5 = 27.5 x 2

=>2x = 55 - 5

=> x =

$\dfrac{50}{2} = 25$

Hence,

x = 25.

Answer no 5:

Value of y = 8

Explanation:

Given

X=1,2,3,4,5

F=4,5,x,1,2

Mean =2.6

We know that,

Mean =€fx/€f

So,

2.6=(1x4+2x5+3xy+4x1+5x2)/4+5+y+1+2

2.6=(4+10+4+10+3y)/12+y

2.6=(28+3y)/12+y

2.6(12+y)=(28+3y)

31.2+2.6y=28+3y

31.2-28=3y-2.6y

3.2=0.4y

y =3.2/0.4

y = 8

Hence,

The value of y is 8.