Question

The mean of 40 observations is 160. While cross checking it was found that the observation 165 has wrongly been read as 125. Find the new correct mean​

Answer 1

Answer:

Here,

n=40,X= 160

So, X=n1 (∑xi)

160=1/40 (∑xi)

∑xi=6400

Therefore, incorrect value of ∑xi=400

Now

Correct value of ∑xi=6400−125+165=6440

Therefore,

= 6400/40=161 

Step-by-step explanation:

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Answer 2

Let the speed of the boat in still water be x km/hr and the speed of the stream but y km/hr. Then,

Speed upstream =(x−y)km/hr

Speed downstream =(x+y) km/hr

Now, Time taken to cover 32km upstream = x−y32

hrs

Time taken to cover 36 km downstream = x+y36

hrs

But, total time of journey is 7 hours.

∴

x−y

32

+

x+y

36

=7 ..(i)

Time taken to cover 40km upstream =

x−y

40

Time taken to cover 48 km downstream =

x+y

48

In this case, total time of journey is given to be 9 hours.

∴

x−y

40

+

x+y

48

=9 (ii)

Putting x−y1

=u and x+y1

=v in equations (i) and (ii), we get

32u+36v=7⇒32u−36v−7=0 ..(iii)

40u+48v=9⇒40u−48v−9=0 ..(iv)

Solving these equations

Let the speed of the boat in still water be x km/hr and the speed of the stream but y km/hr. Then,

Speed upstream =(x−y)km/hr

Speed downstream =(x+y) km/hr

Now, Time taken to cover 32km upstream =x−y32 hrs

Time taken to cover 36 km downstream =x+y36 hrs

But, total time of journey is 7 hours.

∴x−y32+x+y36=7 ..(i)

Time taken to cover 40km upstream =x−y40

Time taken to cover 48 km downstream =x+y48

In this case, total time of journey is given to be 9 hours.

∴x−y40+x+y48=9 (ii)

Putting x−y1=u and x+y1=v in equations (i) and (ii), we get

32u+36v=7⇒32u−36v−7=0 ..(iii)

40u+48v=9⇒40u−48v−9=0 ..(iv)

Solving these equations by cross-multiplication, we get

36×−9−48×−7u=32×−9−40×−7−v=32×48−40×361

⇒−324+336u=−288+280−v=1536−14401

⇒12u=8v=961

⇒u=9612 and v=968

⇒u=81 and v=121

Now, u=81⇒x−y1=81⇒x−y=8 ..(v)

and, v=121⇒x+y1=121⇒x+y=12 ..(