Question

The median of the following observation arranged in ascending order is 40. find x 15, 12, 11, 14, x + 2, x + 4, 32, 30, 41, 35

Answer 1

Answer:

we know,

if the number of observation (n) is even

then,

1. first of all find the value at the position \{\frac{n}{2}\}{2n}

2. and find the value at the position \{\frac{n}{2}+1\}{2n+1}

3. now find the average of two value to get the median .

e.g., \text{median}=\frac{\{\frac{n}{2}\}th+\{\frac{n}{2}+1\}th}{2}median=2{2n}th+{2n+1}th

Given, 11, 12, 14, 18, (x + 2), (x + 4) , 30, 32 , 35 , 41 are in ascending order .

number of terms = 10 {even}

so, median = {(n/2)th + (n/2 + 1) th }/2

24 = (5th + 6th)/2

24 = {(x + 2) + (x + 4)}/2

24 = (x + 3)

x = 21

hence, x = 21

Answer 2

Answer:

x= 16

Step-by-step explanation:

given

median = 40

n = 10

since 'n'is even

therefore ,

median = ( n/ 2) th observation + ( n/2 + 1 ) / 2 th observation

40= ( 10/ 2) the observation+ ( 10/2+1)/2th observation

40×2= 5th observation+ 6th observation

80= (x+2)+(×+4)

80=2x+6

80-6=2x

therefore ,

x=72/2

x= 16