Question

If V is the variance and M is the mean of first 15 natural numbers,then what is V+M×M equals to ?????​

Answer 1

Answer:

first 15 natural numbers

1,2,3,4,5,6,7,8,9,10,11,12,13,14,151,2,3,4,5,6,7,8,9,10,11,12,13,14,15

N=5N=5

mean,

\mu =\dfrac{1}{N}\sum_{i=1}^{N}x_iμ=

N

1

∑

i=1

N

x

i

\mu =\dfrac{1}{15}(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15)μ=

15

1

(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15)

=\dfrac{120}{5}=8=

5

120

=8

variance,

\sigma ^2=\dfrac{1}{N}\sum_{i=1}^{N}(x_i-\mu )^2σ

2

=

N

1

∑

i=1

N

(x

i

−μ)

2

=\dfrac{1}{15}\sum_{i=1}^{15}(x_i-8 )^2=

15

1

∑

i=1

15

(x

i

−8)

2

=\dfrac{1}{15}(280)=

15

1

(280)

Given,

V+M^2V+M

2

=\dfrac{280}{15}+8^2=

15

280

+8

2

=\dfrac{1240}{15}=

15

1240

=\dfrac{248}{3}=

3

248