Question

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}

Answer 1

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

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 .