Question

If 12 is replaced with 3 in the following set what will happen with the value of the range 28,45,12,34,36,45,19,20

Answer 1

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

Answer 2

Answer:

the range will increase from 12-45 to 3-45 to your range will be higher.