According to the chart shown, which of the following is

Dummies like myself tend to start questions from the basics

Before starting, you need to know how to calculate the Median value - The Median is the "middle number" (in a sorted list of numbers).

To find the Median number, you need to know how many numbers there are in a set, its' total could either be even or odd.
For example

Set 1 ( 2, 5, 6, 7, 8 ) = 5 numbers (odd), the Median value is the 3rd number, 5.

Set 2 ( 2, 4, 6, 8, 10, 11) = 6 numbers (even)0, the Median value is average of the two middle valudes, e.g. (6+8)/2= 7

In the question, 1990 - 2000, there are 11 (odd) numbers in the chart, you will have to sort their values from the lowest to the highest and count the 6th number.

Year '000
1 1991 180
2 1990 190
3 1992 210
4 1993 270
5 2000 270
6 1994 310
7 1995 350
8 1999 360
9 1997 370
10 1996 380
11 1998 390

The correct answer is C

Thanks

I'm sorry I feel very foolish for getting this wrong and I'm sure this question will sound just as foolish.

I correctly found which bar was the Median bar on the graph (because I know how to find the median) but then estimated that the value of that bar was 325,000 (D). Am I just supposed to be better at reading graphs to know that it's supposed to be 310? I just don't understand how I'm supposed to know that the median bar on the graph is 310 without any other numerical help besides the 100,000 increments on the right. I would definitely get this wrong on the real exam for the same reason.

Well, 6th tallest bar, is a bit more than 300,000 so approximately 310,000.

325,000 would be 300,000 and 1/4th of the increment and the bar for 1994 is less than that.

I marked it E, because the 6th bar is nowhere close to 300,000, its seems to be close to 350,000, or at best close to 325,000. I still feel that the answer choice C is wrong.

Please re-read the solution. We need the value of 6th tallest bar NOT 6th bar from.

Solution:

An easy way to determine which data value is the median is to take the total number of shipments, add 1, and then divide by 2:

(11 + 1)/2 = 6

Thus, the median will be the 6th shipment. (Remember, we will have to list the data values in ascending order, and the 6th value will be the median.)

We can always use the above method of determining the median when we have an odd number of terms.

Let’s start by ordering the approximate number of shipments from least to greatest with the year in parentheses. Since we know the median is the 6th shipment, we can stop once we get to the 6th term.

1) 180,000 (1991)

2) 190,000 (1990)

3) 210,000 (1992)

4) 280,000 (1993)

5) 280,000 (2000)

6) 305,000 (1994)

We see that 305,000 is the median number of shipments, which is closest to 310,000.

The answer is C.

Hello experts,
VeritasKarishma, EMPOWERgmatRichC, ArvindCrackVerbal, AaronPond, GMATinsight
If someone (student) has a little bit eye problem, how s/he make decision between C and D?
Thanks__

Hello Asad,

I'll refrain from commenting on the biological constraints that a student might have. However, he/she can certainly improve his/her estimation and approximation skills.

In a bar graph like the one in this question, learn to observe the intervals in the vertical direction (the horizontal axis represents ‘Time’ most often) . In this graph, the interval is that of 100,000 units.

Once this is done, you need to have certain fixed points like the below:

If the top of a bar is exactly in between the upper and the lower interval, it is 50,000. This is the halfway mark.

If the top of a bar is exactly in between the halfway mark and the lower interval, take it as 25,000.

If the top of a bar is exactly in between the halfway mark and the upper interval, take it as 75,000.

Now, we come to the most interesting part which has probably necessitated this question. What if the bar ends just above the lower interval? Or just below the upper interval?

For example, what would be the value for 1990? I’d take it as 190,000. What about 1994, you ask! I’d take 310,000. How about 1992? I’d assume it as 220,000 but if you assumed it as 225,000, our answers would not be a world apart.

Remember that if you find a similar question on the GMAT, the question will probably accommodate the fact that two different students will interpret the same bar in the way we did. As such, the answer options may not be really very close for you to worry about going wrong if your estimation was slightly off. In fact, in a lot of questions, GMAT expects you to approximate/estimate and rewards you if you do.

So, do not worry about your approximated values not matching exactly with someone else’s, as long as you are not making vague approximations.

Hope that helps!

Hi Asad,

To start, I'm going to assume that the person that you referred to would be able to tell when one of the lines was slightly above a certain point (for example, the bar for 1992 is slightly above the 200,000 line) and when a line is slightly below a certain point (for example, the bar for 1990 is slightly below the 200,000 line). In addition, I'll assume that this person knows the definition of the word "median" and that he/she knows that the median is represented by the bar for 1994.

So the question is really "is the bar for 1994 approximately 310,000 or 325,000 - and how would you know for sure (especially if your vision isn't great)?" The best that any of us could reasonably do under these circumstances is to put your pen on the screen and look for 2 marks:

1) Where is the half-way point between 300,000 and 400,000? Note that that is approximately 350,000.
2) Using your prior mark for 350,000.... what is the half-way point between 300,000 and 350,000? That is approximately 325,000.

Now, compare your second mark to the bar for 1994. Is your mark at the exact same level as the bar (then choose 325,000) or is your mark a little higher than the bar (then choose 310,000)? If a person's visual acuity is so bad that making this type of deduction is too difficult, then that's unfortunate. It's worth noting that no individual question will keep you from scoring at a really high level though, so getting this question wrong won't "kill" your Score. In addition, choosing between Answers C and D is still a 50/50 shot (which is as good as things can get when you don't know for sure what the correct answer is).

GMAT assassins aren't born, they're made,
Rich

Use the straight edge of your scratch pad to hold the half point mark (between 300 and 400). Now note that the 1994 bar is lower than the half of 300 - 350 gap. I am not sure how the eye problem hinders approximation and hence how you can fix it, but this is one method I would try if I want to get better approximation.

Bunuel chetan2u VeritasKarishma EMPOWERgmatRichC


Basic confusion please.

Isn't number of shipments 'frequency' ? Why are we arranging 'frequency' in ascending order when the years themselves are in ascending order.

I am relating this question's graph to the one in this video here. Can someone please point out that how are these two graphs different.

Will be much obliged.

Hi altairahmad,

The chart in this question and the chart in the video you linked have one significant difference between them: In this prompt, each vertical line refers to ONE number (not a 'frequency'), but in the video, each vertical line refers to a number that appears between 2 and 12 times, inclusive.

In this prompt, we're asked to find the MEDIAN number of shipments. Since there are 11 numbers to consider, we have to do enough work to arrange the numbers in order to find the 6th value (so we might either find the '6 smallest' or '6 largest'). In the video, we're asked to find the MEDIAN of 50 values, so we need to do enough work to find the AVERAGE of the 25th and 26th numbers. We have to consider the frequency of each interval, since that defines how many times each of the 7 intervals appears (and that will define which interval(s) are the 25th and 26th numbers.

GMAT assassins aren't born, they're made,
Rich

Video solution from Quant Reasoning:
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Answer: Option C

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