Answer:
The interquartile range remains the same.
Step-by-step explanation:
Interquartile range is the difference between first and third quartile.
I.Q.R.=Q_3-Q_1
The given data is
28, 45, 12, 34, 36, 45, 19, 20
Arrange the data is ascending order.
12, 19, 20, 28, 34, 36, 45, 45
(12, 19, 20, 28), (34, 36, 45, 45)
(12, 19), (20, 28), (34, 36), (45, 45)
The first quartile is midpoint of 19 and 20 and the third quartile is the midpoint of 36 and 45.
Q_1=\frac{19+20}{2}=19.5
Q_3=\frac{36+45}{2}=40.5
I.Q.R.=Q_3-Q_1
I.Q.R.=40.5-19.5=21
The interquartile range of given data is 21.
If 12 is replaced with 3 in the following set, then the given data is
3, 19, 20, 28, 34, 36, 45, 45
(3, 19, 20, 28), (34, 36, 45, 45)
(3, 19), (20, 28), (34, 36), (45, 45)
The first quartile is midpoint of 19 and 20 and the third quartile is the midpoint of 36 and 45.
Q_1=\frac{19+20}{2}=19.5
Q_3=\frac{36+45}{2}=40.5
I.Q.R.=Q_3-Q_1
I.Q.R.=40.5-19.5=21
The interquartile range of given data is 21.
The interquartile range remains the same. Therfore option 3 is correct