Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #2

14

# In the course of an experiment, 95 measurements

In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval. Quantity A : The average (arithmetic mean) of the 95 measurements Quantity B : The median of the 95 measurements Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 6 Explanations

1

Abdul Sugair

Hi, please explain how is the mean which is 1015/90 is greater than 48th which is the median???

Sep 16, 2020 • Comment

Hi Abdul,
The median is the 48th number in the set. So it's not 48, it's the value of the 48th number. We don't know the value of that number exactly, but we know it is between 6 and 10. Thus, 10 is the largest number the median could be.

1015/90 ≈ 11.3, which is greater than 10. No matter what, then, the mean is greater than the median.

1

rabab aldeabel

I don't understand why the median is 48th ?

Sep 17, 2018 • Comment

Sam Kinsman

Hi Rabab,

Keep in mind that the median is the middle number in the set (when the numbers are arranged from smallest to largest).

To find where the median is located in the set, take the amount of numbers in the set (we'll call that n), and add 1, and divide by 2:

location of median = (n+1)/2

In this case, there are 95 numbers, so:

(95+1)/2 = 48

That means that the 48th number will be the median number.

I hope this helps! :)

1

Hi ,

What if we have to compare the Standard deviation here ?
Which one would be greater ?

Sep 5, 2018 • Comment

David Recine, Magoosh Tutor

That's really hard to say. Calculating the standard deviation requires very precise measurements. Without exact measurements there can be wildly different outcomes. For example, the mean itself could easily be anywhere between 6 and slightly more than 10, depending on the other individual values in each value interval. And if all of the other unlisted values were as close to the mean as possible, then the standard deviation from the mean would be substantially lower than if the values were as far from the mean as possible.

If you plug in hypothetical values for each interval, you'll be able to "ballpark" how much variety there can be in standard deviation and mean values. For that matter, you'll see a lot of variety in median values too. I recommend playing with the numbers that way, as it can really help you understand how these kinds of stats/DI problems work on the GRE. :)

2

vaishali shetty

what does skewed to the left mean? if it is going towards left doesnt it mean th value is 1-5 which is lesser than 6-10?

Jul 11, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Vaishali :)

"Skewed to the left" means that the long "tail" of the graph is on the left hand side. This is also called a negative skew, as the long tail is on the negative side of the peak.

In the practice problem, the tail is to the right of the peak, which is why we consider the graph skewed to the right.

Hope that helps!

2

CHAHAT RUSTAGI

I am really not clear with the MEAN part! Please re-explain.

Jan 19, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

The mean is the average value of a set of numbers. If we have a symmetrical distribution, the average will be close to the median, or middle number, of that distribution. This is what Chris shows when he discusses what is observed in intervals 1-5, 6-10, and 11-15. Because there are 15 measurements in the 1-5 interval and 15 measurements in the 11-15 interval, if we were to ignore the measurements above the 11-15 interval, we could conclude (without doing any calculations) that the mean will be in the 6-10 interval and very close to the median. The mean could be slightly higher or lower or the same as the median, depending on the exact values within the 6-10 interval.

However, in this problem, because there are values above the 11-15 range, we can determine that the average will be skewed to the left, making the average greater than the median.

I hope this helps! :)

And for more review on mean, median, and mode, check out the following post from our GRE blog :D

http://magoosh.com/gre/2014/mean-median-and-mode-on-the-gre/

10 Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment

jishu kumar dey

i think the graph represents a positively skewed shape and since 1st 3 bar mean is clearly 6-10 .but the presence of some extreme values i mean the last part make the mean greater than 6-10.am i right ?

Cydney Seigerman, Magoosh Tutor

Hi Jishu :)

Yes, you're correct that we have a positively skewed distribution. Since we have values greater than 11-15, we can conclude that the average will be greater than the median :)