Which data set has the greatest spread for the middle 50% of its data? a. {18, 13, 22, 17, 21, 24} b. {17, 19, 22, 26, 17, 14} c. {13, 17, 12, 21, 18, 20} d. {18, 21, 16, 22, 24, 15}

{13, 17, 12, 21, 18, 20} has the greatest spread for the middle 50% of its data.

Step-by-step explanation:

Given:

Set 1={18, 13, 22, 17, 21, 24}

Set 2={17, 19, 22, 26, 17, 14}  

Set 3= {13, 17, 12, 21, 18, 20}

Set 4=  {18, 21, 16, 22, 24, 15}

To find :

Data set has the greatest spread for the middle 50% of its data=?

Solution:

Step 1:  Re arranging the data sets in ascending order

Re-arranging data-set 1 we get,

{13, 17, 18, 21, 22, 24}

Re-arranging data-set 2 we get,

{14, 17, 17, 19, 22 , 26}

Re-arranging data-set 3 we get,

{12, 13, 17, 18, 20, 21}

Re-arranging data-set 4 we get,

{15, 16,18, 21, 22, 24}

Step 2 : Finding the interquantile region:

Interquantile Range(IQR) = lower median-upper median

For data-set 1

IQR=22-17=5

For data-set 2

IQR=22-17=5

For data-set 3  

IQR=20-13=7

For data-set 4

IQR=22-16=6

Hence the data set 3 = {13, 17, 12, 21, 18, 20} has greatest spread for the middle 50% of its data .

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕