Question

1. (05.02 mc)

the employees of two companies were asked how many times they checked their email during weekends. the table shows the numbers for each company:
company a 2 4 8 8 2 6 4 8 3
company b 2 6 3 5 2 4 6 3 2
based on the table, which of the following is true? (1 point)
the interquartile range for company a employees is 2 more than the interquartile range for company b employees.
the interquartile range for company a employees is 0.5 more than the interquartile range for company b employees.
the interquartile range for company a employees is 1 more than the interquartile range for company b employees.
the interquartile range for company a employees is 2.5 more than the interquartile range for company b employees.

Explanation:

Step1: Sort Company A data

Sorted Company A: $2, 2, 3, 4, 4, 6, 8, 8, 8$

Step2: Find Company A quartiles

$n=9$, median ($Q_2$) = 5th value = $4$
Lower half: $2,2,3,4$, $Q_1 = \frac{2+3}{2}=2.5$
Upper half: $6,8,8,8$, $Q_3 = \frac{8+8}{2}=8$
IQR (A) = $Q_3 - Q_1 = 8 - 2.5 = 5.5$

Step3: Sort Company B data

Sorted Company B: $2, 2, 3, 3, 4, 5, 6, 6, 3$ → corrected sorted: $2,2,3,3,4,5,6,6,3$ → final sorted: $2,2,3,3,4,5,6,6,3$ → correct sorted: $2,2,3,3,4,5,6,6,3$ → fixed: $2,2,3,3,3,4,5,6,6$

Step4: Find Company B quartiles

$n=9$, median ($Q_2$) = 5th value = $3$
Lower half: $2,2,3,3$, $Q_1 = \frac{2+3}{2}=2.5$
Upper half: $4,5,6,6$, $Q_3 = \frac{5+6}{2}=5.5$
IQR (B) = $5.5 - 2.5 = 3$

Step5: Calculate IQR difference

Difference = $5.5 - 3 = 2.5$

Answer:

The interquartile range for Company A employees is 2.5 more than the interquartile range for Company B employees.