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The lengths of each of the segments connected by the given pairs of points are:
1. AB = 10 units
2. CD = 17 units
3. EF = 3 units
<h3>How to Find the Length of Segments Connected by Two Points?</h3>To find the length of a segment connected by two coordinate points, the distance formula is applied, which is:
d = .
1. Find the length of segment AB:
A(5,-3)
B(-3,3)
AB = √[(−3−5)² + (3−(−3))²]
AB = √[(−8)² + (6)²]
AB = √100
AB = 10 units
2. Find the length of segment CD:
C(-2, -7)
D(6, 8)
CD = √[(6−(−2))² + (8−(−7))²]
CD = √(64 + 225)
CD = 17 units
3. Find the length of segment EF:
E(5,6)
F(5,3)
EF = √[(5−5)² + (3−6)²[
EF = √(0 + 9)
EF = √9
EF = 3 units
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Solution:
Data represented as number of hours spent in studying by Group A Students:
1,2,1,1,3,3,2,2,3
Arranging it in ascending order: 1,1,1 ,2, 2, 2, 3, 3, 3,
As number of terms is odd, The median will be middle value of observation.Which is 2.
The Data arranged in ascending order are , (1,1,1,2),2(2,3,3,3).
Median of (1,1,1,2) = =1
Median of (2,3,3,3)==3
=Interquartile Range =
=3-1=2
For Data Set 2,
The Data for group B students are: 3 2 3 2 2 2 1 1 2
Arranging in ascending order: 1,1,2,2,2,2,2,3,3
total number of observation = 9
Median = 2
Arranging the data as : (1,1,2,2) 2,(2,2,3,3)
Median of (1,1,2,2)= Number of observation is 4 which is even , so Median= =
Median of (2,2,3,3)==
S=Interquartile Range = =
Interquartile range for Group A Students =Interquartile range for Group B students + 1
Option (D) The interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.