70 students responded to a survey documenting the amount of time spent

Question

70 students responded to a survey documenting the amount of time spent on television.
The results are summarized in the graph as follows:

8 watched fewer than 1 hr of TV per week, 4 watched at least 1 hour but less than 2, and so on.

Based on the given information, use the drop-down menus to most accurately complete the following statements.

1. The least possible value for the mean of the numbers of hours of TV reported for the week is .

2. The number of respondents who watched on average less than 3/4 hour per day during the week is between .

Show Spoiler

Attachment:

1.jpg [ 38.85 KiB | Viewed 5290 times ]

Submit Answer

Start the Timer above, select the dropdowns, and click "Submit" to add this question to your Error log.

Show Answer

Official Answer

Dropdown 1: 4.07 Dropdown 2: 40 and 51

macjas · Accepted Answer

Let me see:

A) In order, to get the least possible value of the average number of TV viewing hours, lets assume that those people who watch less than 1 hour a day actually watch 0 hours. By doing this, we will effectively lower the average.

Let's calculate the average:

\(\frac{0(8)+1(4)+2(8)+3(9)+4(11)+5(11)+6(7)+7(8)+10(3)+11(1)}{70}\)

\(= \frac{285}{70} = 4.0714\)

So A must be 4.07

B) The respondents that watched less than 3/5 hrs a day watched less than\(\frac{{7*3}}{4} = 5.25\) hrs a week.

So the number of people who watched less than 5.25 hrs a week would include more or less those people to the left of the arrow below:

Attachment:

Capture.JPG [ 43.5 KiB | Viewed 6467 times ]

So for now, lets ignore the bar with the arrow.

The number of people to the left of the bar (excluding the bar) is:

8+4+8+9+11 = 40

Now, the bar with the arrow: 11 people watched at least 5 hours but less than 6hrs. If they did watch 5 hrs or less we can count them in our calculations. However, it is also possible that they could have watched 5.8hrs in which case we don't count them.

So our range is 40 (if we don't count them) to 51(if we do)

skyhi · Answer

Hi Experts 
please help with this question.

I could do the 1st part same way mentioned in the above post but that will take a long time for calculation.

for the 2nd part we can calculate who watched for >= 3/4 and substract. that would be quicker.

macjas · Answer

Hi Mayank

Pretty straightforward:

3/4 hrs a day * 7 days = 5.25 hours a week. Did the typo in my previous post confuse you? (it needs to be 3/4 not 3/5)?

Other than this, I can't explain it any better than how I did in the last post. Perhaps some expert can chime in?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

70 students responded to a survey documenting the amount of time spent

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Graphs and Tables (G&T) Questions

70 students responded to a survey documenting the amount of time spent

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards