Question

median and mode for 10 observations are 15 and 25 respectively.if each observation is increased by 8, what will be the change in value of mode and median?​

Answer 1

Answer:

Let the given observations x1,x2,x3,x4,x5,x6.

Then, mean =8⇒16(x1+x2+x3+x4+x5+x6)=8

⇒ x1+x2+x3+x4+x5+x6=48. (i)

Also, variance =16

⇒ 16(x21+x22+x23+x24+x25+x26)−82=16 [∵σ2=Σx2in−(x¯)2]

⇒ x21+x22+x23+x24+x25+x26=480. ...(ii)

When each observation is multiplied by 3, then new observations are

3x1,3x2,3x3,3x4,3x5and3x6.

∴ new mean =16(3x1+3x2+3x4+3x5+3x6)

=36(x1+x2+x3+x4+x5+x6)=(12×48)=24 [using (i)]  

∴ new variance (3x1)2+(3x2)2+(3x3)2+(3x4)2+(3x5)2+(3x6)26−(24)2

=96(x21+x22+x23+x24+x25+x26)−576

=(96×480)−576=(720−576)=144 [using (ii)].

Step-by-step explanation:

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