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14 May 2020, 00:41
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For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths.: Yes
More than half of the 22 earthquakes occurred north of the equator.: No
Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT.: No
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
88% (02:46) correct
12%
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wrong
based on 776
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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.
For each of the following statements, select Yes if the statement is true based on the information provided; otherwise, select No.
| 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.
| Yes | No | |
| For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths. | ||
| More than half of the 22 earthquakes occurred north of the equator. | ||
| Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT. |
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Official Answer
For the 22 earthquakes, the arithmetic mean of the depths is greater than the median of the depths.: Yes
More than half of the 22 earthquakes occurred north of the equator.: No
Exactly half of the earthquakes listed occurred between 10:00:00 and 20:00:00 GMT.: No
26 Apr 2021, 04:10
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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.
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.
General Discussion
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14 May 2020, 11:58
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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.
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.
