Mean of eight observations is 25. If one observation 11 is excluded , find the mean of the remaining.​

Mean = 27

Step-by-step explanation:

Given mean = 25

No of observations (N) = 8

We know,

Mean = Sum / N

25 = Sum / 8

Sum = 25 x 8

Sum = 200

Since an observation 11 is removed,

New sum = 200 - 11 = 189

New no. of observation (N) = 8 - 1 = 7

Now,

Mean of remaining observations = New Sum / New N

= 189/7

= 27

mean=25

n=8

sum of observation=?

we have

mean=sum/n

sum=25×8=200

if one observation is excluded

sum will be =200-11=189

[n]no of observation = 8-1=7

new mean =new sum/new n=189/7=27

the mean of the remaining is 27

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9