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The help desk is keeping track of the number of minutes the average caller spends on hold.

\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Average Time on Hold with Help Desk} \\
\hline
Week & \begin{tabular}{c}
Average Time on Hold \\
(Minutes)
\end{tabular} \\
\hline
1 & 7 \\
\hline
2 & 5 \\
\hline
3 & 3 \\
\hline
4 & 2 \\
\hline
5 & 3 \\
\hline
6 & 5 \\
\hline
\end{tabular}

According to the table, during which interval did the average time spent on hold increase?

A. week 1 to week 3

B. week 1 to week 4

C. week 4 to week 6

D. week 3 to week 5



Answer :

GinnyAnswer
To determine the intervals during which the average time spent on hold increased, we need to analyze the changes in the average hold time from week to week.

Let's look at the average hold times given for each week:
- Week 1: 7 minutes
- Week 2: 5 minutes
- Week 3: 3 minutes
- Week 4: 2 minutes
- Week 5: 3 minutes
- Week 6: 5 minutes

First, we calculate the differences in hold times between consecutive weeks:
- Week 2 - Week 1: [tex]\(5 - 7 = -2\)[/tex] minutes (a decrease)
- Week 3 - Week 2: [tex]\(3 - 5 = -2\)[/tex] minutes (a decrease)
- Week 4 - Week 3: [tex]\(2 - 3 = -1\)[/tex] minutes (a decrease)
- Week 5 - Week 4: [tex]\(3 - 2 = 1\)[/tex] minute (an increase)
- Week 6 - Week 5: [tex]\(5 - 3 = 2\)[/tex] minutes (an increase)

Now, we need to look at the specified intervals and determine if the average hold time increased in those intervals:

1. Week 1 to Week 3:
- Calculate the total change from Week 1 to Week 3:
[tex]\[ (Week 2 - Week 1) + (Week 3 - Week 2) = -2 + (-2) = -4 \text{ minutes (a decrease)} \][/tex]

2. Week 1 to Week 4:
- Calculate the total change from Week 1 to Week 4:
[tex]\[ (Week 2 - Week 1) + (Week 3 - Week 2) + (Week 4 - Week 3) = -2 + (-2) + (-1) = -5 \text{ minutes (a decrease)} \][/tex]

3. Week 4 to Week 6:
- Calculate the total change from Week 4 to Week 6:
[tex]\[ (Week 5 - Week 4) + (Week 6 - Week 5) = 1 + 2 = 3 \text{ minutes (an increase)} \][/tex]

4. Week 3 to Week 5:
- Calculate the total change from Week 3 to Week 5:
[tex]\[ (Week 4 - Week 3) + (Week 5 - Week 4) = -1 + 1 = 0 \text{ minutes (no change)} \][/tex]

From this analysis, we can conclude that the only interval during which the average time spent on hold increased is:

week 4 to week 6.

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