Mathematics, 13.11.2019 10:31 pineappledogpie1608

If 12 is replaced with 3 in the following set, what will happen to the value of the interquartile range? 28, 45, 12, 34, 36, 45, 19, 20 it will increase. it will decrease. it will stay the same.

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Answer from: oceanbrezze85

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 from: sukhmanksidhu

It will stay same.

Step-by-step explanation:

The given data is:

28, 45, 12, 34, 36, 45, 19, 20.

In order to find the interquartile range, first arrange them given data in ascending order, we get

12,19 ,20, 28, 34, 36, 45, 45.

Now, calculate the median of the above data, we get

Median= $\frac{28+34}{2}=\frac{62}{2}=31$

Now, find the median of the upper and the lower half.

Median of Upper half: $\frac{36+45}{2}=\frac{81}{2}$ and

Median of lower half: $\frac{19+20}{2}=\frac{39}{2}$

The interquartile range of this data is : Median of Upper half- median of lower half= $\frac{81}{2}-\frac{39}{2}=21$ .

Now, if we replace 12 with 3 in the given data, we get

3, 19 ,20, 28, 34, 36, 45, 45 in ascending order.

Now, calculate the median of the above data, we get

Median= $\frac{28+34}{2}=\frac{62}{2}=31$

Now, find the median of the upper and the lower half.

Median of Upper half: $\frac{36+45}{2}=\frac{81}{2}$ and

Median of lower half: $\frac{19+20}{2}=\frac{39}{2}$

The interquartile range of this data is : Median of Upper half- median of lower half= $\frac{81}{2}-\frac{39}{2}=21$ .

Itcan be seen that the interquartile range remains the same even after replacing 12 with 3.

Therefore, the interquartile range will remain the same.

Answer from: Quest

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.
Which table shows a proportional relationship between x and y

Which table shows a proportional relationship between x and y

Answer from: Quest

c: y > - 1/6x + 1

step-by-step explanation:

dashed line - meaning this < or > also not equal

solid line - meaning this < or > also equal

your answer is c because y > means up & it's shaded up, but y < means down

hope this ! : )

Which inequality is represented by the graph? (0,1) (6,0)

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