Question

question 5 (1 point)mc:radio:(05.02 mc)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 3group b 3 2 3 2 2 2 1 1 2based on the table, which of the following is true?a the interquartile range for group a students is 0.5 less than the interquartile range for group b students.b the interquartile range for group a students is 1.5 more than the interquartile range for group b students.c the interquartile range for group a students is equal to the interquartile range for group b students.d the interquartile range for group a students is 1 more than the interquartile range for group b students.

Explanation:

Step1: Sort Group A data

Sorted Group A: $1, 1, 1, 2, 2, 3, 3, 4, 5$

Step2: Find Group A quartiles

$n=9$, median ($Q_2$) = 5th value = $2$
$Q_1$ = median of lower half ($1,1,1,2$) = $\frac{1+1}{2}=1$
$Q_3$ = median of upper half ($3,3,4,5$) = $\frac{3+4}{2}=3.5$
Interquartile Range (IQR) for A: $Q_3-Q_1=3.5-1=2.5$

Step3: Sort Group B data

Sorted Group B: $1, 1, 2, 2, 2, 2, 3, 3, 2$ → corrected sorted: $1,1,2,2,2,2,2,3,3$

Step4: Find Group B quartiles

$n=9$, median ($Q_2$) = 5th value = $2$
$Q_1$ = median of lower half ($1,1,2,2$) = $\frac{1+2}{2}=1.5$
$Q_3$ = median of upper half ($2,2,3,3$) = $\frac{2+3}{2}=2.5$
Interquartile Range (IQR) for B: $Q_3-Q_1=2.5-1.5=1$

Step5: Compare IQRs

Difference: $2.5-1=1.5$

Answer:

b. The interquartile range for Group A students is 1.5 more than the interquartile range for Group B students.