Question

Two groups of students were asked how many pets they had. The table shows the numbers for each group: Group A 1 2 1 1 3 5 4 2 3 Group B 3 2 3 2 2 2 1 1 2 Based on the table, which of the following is true? The interquartile range for Group A students is 0. 5 less than the interquartile range for Group B students. The interquartile range for Group A students is 1. 5 more than the interquartile range for Group B students. The interquartile range for Group A students is equal to the interquartile range for Group B students. The interquartile range for Group A students is 1 more than the interquartile range for Group B students.

Answer 1

The interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.

Given

Data represented as a number of hours spent 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 a number of terms are odd,

The median will be the middle value of observation.

Which is 2.

What is the interquartile range?

The interquartile range (IQR) is the range of values that resides in the middle of the scores.

The Data arranged in ascending order are; (1,1,1,2,2,2,3,3,3).

Median of (1, 1, 1, 2) = 1 $\rm Q_1=1$

Median of (2, 3, 3, 3) =3 $\rm Q_3=3$

Interquartile Range = $\rm Q_3-Q_1$ = 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

The total number of observations = 9

Median = 2

Arranging the data as : (1,1,2,2) 2,(2,2,3,3)

Median of (1,1,2,2)= Number of observations is 4 which is even;

$\rm Median = \dfrac{1+2}{2}\\\\Median = \dfrac{3}{2}$

Median of (2,2,3,3) = $\rm Q_3 =\dfrac{3+2}{2} = \dfrac{5}{2}$

S = Interquartile Range = $\rm Q_3-Q_1=\dfrac{5}{2}-\dfrac{3}{2}=1$

The interquartile range for Group A Students =Interquartile range for Group B students + 1.

$\rm D=S_1+1$

Hence, the interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.

To know more about interquartile range click the link given below.

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