The table lists data on the 22 earthquakes of magnitude 7 or greater o

Question

The table lists data on the 22 earthquakes of magnitude 7 or greater on the Richter Scale during a recent year. Times are given in hours, minutes, and seconds on the 24-hour Greenwich Mean Time (GMT) clock and correspond to standard time at Greenwich, United Kingdom (UK). Latitude, measured in degrees, is 0 at the equator, increases from 0 to 90 proceeding northward to the North Pole, and decreases from 0 to -90 proceeding southward to the South Pole. Longitude, also measured in degrees, is 0 at Greenwich, UK, increases from 0 to 180 from west to east in the Eastern Hemisphere, and decreases from 0 to -180 from east to west in the Western Hemisphere.

Date (month/day)  
  Time (GMT)  
  Magnitude  
  Depth (km)  
  Latitude  
  Longitude  
 
   1/03  
 22:36:28 
 7.1 
 25 
 -8.799 
 157.346 
 
   01/12  
 21:53:10 
 7.0 
 13 
 18.443 
 -72.571 
 
   02/26  
 20:31:27 
 7.0 
 25 
 25.93 
 128.425 
 
   02/27  
 06:34:12 
 8.8 
 23 
 -36.122 
 -72.898 
 
   04/04  
 22:40:43 
 7.2 
 4 
 32.297 
 -115.278 
 
   04/06  
 22:15:02 
 7.8 
 31 
 2.383 
 97.048 
 
   05/09  
 05:59:42 
 7.2 
 38 
 3.748 
 96.018 
 
   05/27  
 17:14:47 
 7.1 
 31 
 -13.698 
 166.643 
 
   06/12  
 19:26:50 
 7.5 
 35 
 7.881 
 91.936 
 
   06/16  
 03:16:28 
 7.0 
 18 
 -2.174 
 136.543 
 
   07/18  
 13:34:59 
 7.3 
 35 
 -5.931 
 150.59 
 
   07/23  
 22:08:11 
 7.3 
 607 
 6.718 
 123.409 
 
   07/23  
 22:51:12 
 7.6 
 586 
 6.486 
 123.467 
 
   07/23  
 23:15:10 
 7.4 
 641 
 6.776 
 123.259 
 
   08/04  
 22:01:44 
 7.0 
 44 
 -5.746 
 150.765 
 
   08/10  
 05:23:45 
 7.3 
 25 
 -17.541 
 168.069 
 
   08/12  
 11:54:16 
 7.1 
 207 
 -1.266 
 -77.306 
 
   09/03  
 16:35:48 
 7.0 
 12 
 -43.522 
 171.83 
 
   09/29  
 17:11:26 
 7.0 
 26 
 -4.963 
 133.76 
 
   10/25  
 14:42:22 
 7.8 
 20 
 -3.487 
 100.082 
 
   12/21  
 17:19:41 
 7.4 
 14 
 26.901 
 143.698 
 
   12/25  
 13:16:37 
 7.3 
 16 
 -19.702 
 167.947

For each of the following statements, select  Yes  if the statement is true based on the information provided; otherwise, select  No .

Sajjad1994 · Accepted Answer

Official Explanation

For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths.

Sorting on Depth (km)  produces a list of earthquakes in increasing order of depth. The median depth (in km) of the 22 earthquakes is the arithmetic mean of the 11th and 12th earthquakes appearing in the list, that is, 1/2(25+26)=25.5.1225+26=25.5. The arithmetic mean of the depths is 1/22 times the sum of all 22 depths; therefore, it must be greater than 1/22 times the greatest depth listed. But this last value—that is, 1/22(641)km, or 29 \frac{3}{22}  km—is already greater than the median depth, so the arithmetic mean of the depths must be greater than the median of the depths.

The correct answer is Yes.

More than half of the 22 earthquakes occurred north of the equator.

A given location is north of the equator provided that its latitude is positive, so it is helpful to  sort on Latitude.  Only 10 of the 22 earthquakes listed occurred at positive latitude, so fewer than half of the earthquakes occurred north of the equator.

The correct answer is No.

Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT.

To determine the number of earthquakes occurring between 10:00:00 and 20:00:00 GMT, it suffices to  sort on Time (GMT)  and then count. The 9 earthquakes appearing in positions 5 through 13 of the sorted list meet the criterion, and  \frac{9}{22}≠\frac{1}{2}

The correct answer is No.

bM22 · Answer

1. For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths.

The depth in ascending order: 4,12,13,14,16,18,20,23,25,25,25,26,31,31,35,35,38,44,207,586,607,641.
Median: (25+26)/2 = 25.5
Mean: 2476/22 = 112.5 
=> Mean > Median.

Answer Yes.

2. More than half of the 22 earthquakes occurred north of the equator.
We can infer from the table that: only 10 out of 22 earthquakes occurred north of the equator.
=> That the given statement is false.

Answer No.

3.Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT.
We can infer from the table that: only 8 out of 22 earthquakes occurred between 10:00:00 and 20:00:00 GMT.
This statement is again false, so No.

Answer is No.

Apt0810 · Answer

1)Yes,if we arrange the depth in ascending order and calculate the median and mean then:

Median =25+26/2=25.5
Mean=2476/22=112.5

2)No,since only 10/22 occured in north of Equator.

3)No,Only 9/22 occured between 10 and 20 GMT

Posted from my mobile device

robu1 · Answer

There is no need to calculate the mean, as three big values affects the sum hugely.

mmdfl · Answer

'"For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths."

We dont need to do any calculation here so say that this statement is true. Just notice that the distribution is strongly biased by some earthquackes with very high depths. This moves the mean to the highest values, but do nothing to the median. More here:  "Skewness and the Mean, Median, and Mode"

shwetakoshija · Answer

Given: A table listing 22 earthquakes (magnitude ≥ 7) shows the following:

Time (GMT)
Depth (km)
Latitude (in degrees): 0 at the equator, 0 to 90 proceeding northward to the North Pole, and 0 to -90 proceeding southward to the South Pole.
Longitude (in degrees): 0 at Greenwich, 0 to 180 from west to east in the Eastern Hemisphere, and 0 to -180 from east to west in the Western Hemisphere.

To Find: The statement(s) that is(are) true based solely on the table.

Solution:
Statement 1: For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths.
MEDIAN:

To find Median of the Depths, first sort the table by the "Depth" column.
Since 22 is an even number, median = average of middle 2 values = average of 11th and 12th values.

Sorted Depth (km): 4, 12, 13, 14, 16, 18, 20, 23, 25, 25, 25, 26, and so on.
Median = (25 + 26)/2 = 25.5

MEAN:

Arithmetic Mean of Depths = (Sum of all depths)/22
Note that the depths are mostly less than 50 but there are four that are greater than 200 each. In fact, two of these are above 600.
So, the sum is already greater than 200 + 200 + 600 + 600 (very rough estimates) = 1600.
Hence, mean > 1600/22 = 72 (approx.).

So, Arithmetic Mean of Depths > Median.

We mark "Yes"

Statement 2: More than half of the 22 earthquakes occurred north of the equator.
By definition of latitude, it is 0 degrees at the equator and goes from 0 to 90 degrees proceeding northward to the North Pole. So:

A given location is north of the equator if its latitude is positive (latitude > 0)

Sort the table by the “Latitude” column to separate positive and negative values.
Counting positive latitudes, we find that only 10 of the 22 earthquakes listed occurred at a positive latitude.
Since half of 22 = 11 and 10 < 11, this statement is not true.

We mark "No"

Statement 3: Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT.

Sort the table by the “Time (GMT)” column.

Now, count the earthquakes with time between 10:00:00 and 20:00:00.
We find a total of 9 such earthquakes in this range (from 11:54:16 to 19:26:50)
Since half of 22 = 11 and 9 < 11, this statement is not true.

We mark "No"

Correct Answers: Yes, No, No

Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years

egmat · Answer

Hi there,

Let me walk through each statement using the table data.

Statement 1 (Mean depth > Median depth): YES

First, sort all  22  depth values in ascending order:
 4 ,  12 ,  13 ,  14 ,  16 ,  18 ,  20 ,  23 ,  25 ,  25 ,  25 ,  26 ,  31 ,  31 ,  35 ,  35 ,  38 ,  44 ,  207 ,  586 ,  607 ,  641

The  median  of  22  values is the average of the  11 th and  12 th values: ( 25  +  26 ) /  2  =  25.5  km.

For the  mean , the sum of all depths is  2,476  km. Dividing by  22  gives approximately  112.5  km. This is far higher than  25.5  because three extreme outliers ( 586 ,  607 ,  641  km from the July  23  earthquakes) pull the mean way up while barely affecting the median. Since  112.5  >  25.5 , the answer is  Yes .

Statement 2 (More than half occurred north of equator): NO

North of the equator means positive latitude. Scanning the Latitude column, the earthquakes with positive latitude are on:  01 / 12 ,  02 / 26 ,  04 / 04 ,  04 / 06 ,  05 / 09 ,  06 / 12 ,  07 / 23  (three times), and  12 / 21 . That is  10  out of  22 . More than half would require at least  12 , so the answer is  No .

Statement 3 (Exactly half occurred between 10:00:00 and 20:00:00 GMT): NO

Exactly half of  22  would be  11  earthquakes. Checking the Time column for times from  10 : 00 : 00  to  19 : 59 : 59  (before  20 : 00 : 00 ):
-  17 : 14 : 47  ( 05 / 27 )
-  19 : 26 : 50  ( 06 / 12 )
-  13 : 34 : 59  ( 07 / 18 )
-  11 : 54 : 16  ( 08 / 12 )
-  16 : 35 : 48  ( 09 / 03 )
-  17 : 11 : 26  ( 09 / 29 )
-  14 : 42 : 22  ( 10 / 25 )
-  17 : 19 : 41  ( 12 / 21 )
-  13 : 16 : 37  ( 12 / 25 )

That is only  9  earthquakes, not  11 . The answer is  No .

Key tip:   For S1,  note that  a few extreme depth values (the three deep earthquakes near  600  km) dramatically inflate the mean while leaving the median almost unchanged. This is a classic GMAT concept —  the mean is sensitive to outliers, the median is not .

Answer: Yes, No, No

The table lists data on the 22 earthquakes of magnitude 7 or greater o

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Date (month/day)	Time (GMT)	Magnitude	Depth (km)	Latitude	Longitude
1/03	22:36:28	7.1	25	-8.799	157.346
01/12	21:53:10	7.0	13	18.443	-72.571
02/26	20:31:27	7.0	25	25.93	128.425
02/27	06:34:12	8.8	23	-36.122	-72.898
04/04	22:40:43	7.2	4	32.297	-115.278
04/06	22:15:02	7.8	31	2.383	97.048
05/09	05:59:42	7.2	38	3.748	96.018
05/27	17:14:47	7.1	31	-13.698	166.643
06/12	19:26:50	7.5	35	7.881	91.936
06/16	03:16:28	7.0	18	-2.174	136.543
07/18	13:34:59	7.3	35	-5.931	150.59
07/23	22:08:11	7.3	607	6.718	123.409
07/23	22:51:12	7.6	586	6.486	123.467
07/23	23:15:10	7.4	641	6.776	123.259
08/04	22:01:44	7.0	44	-5.746	150.765
08/10	05:23:45	7.3	25	-17.541	168.069
08/12	11:54:16	7.1	207	-1.266	-77.306
09/03	16:35:48	7.0	12	-43.522	171.83
09/29	17:11:26	7.0	26	-4.963	133.76
10/25	14:42:22	7.8	20	-3.487	100.082
12/21	17:19:41	7.4	14	26.901	143.698
12/25	13:16:37	7.3	16	-19.702	167.947

GMAT Graphs and Tables (G&T) Questions

The table lists data on the 22 earthquakes of magnitude 7 or greater o

Prep Toolkit

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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