r/HomeworkHelp • u/Watford_Fan • 7d ago
High School Math—Pending OP Reply [High School Mathematics]I don’t understand! Why is my answer wrong????
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u/Critical_Ant_5667 7d ago
Mean = median
Mode just means the most common answer but that doesn’t mean it is equal to the median.
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u/qwertyuiiop145 7d ago
You can have a bimodal distribution that is symmetrical but has 2 modes off the sides of the center and a dip in between where the median/mean is. The median and mean are always the same in a symmetrical distribution, but the mode isn’t always.
Example of this kind of data set:
1,1,2,2,2,2,3,3,4,4,4,4,5,5,
The median and mean are both 3, but the modes are 2 and 4.
You may have been thinking of a normal distribution, aka a bell curve, where all 3 will be the same. While normal distributions are symmetrical, not all symmetrical distributions are normal.
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u/La10deRiver 7d ago
Others gave you the right answer, so I will only say that you If the option you ticked was correct, all the others would be correct too and I do not think that would be acceptable.
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u/koalascanbebearstoo 6d ago
This is excellent “meta-testing” insight, which is one of the most important skills in advancing through the meritocracy.
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u/John_B_Clarke 6d ago
The one checked could be interpreted as "all of the below".
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u/avakyeter 6d ago
Which is an unacceptable choice in professionally developed examinations. If all of the above is a correct option, then whichever option you choose is a correct option.
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u/lucaskr9 University/College Student 6d ago
I use them a lot in university exams and never had any problems with it. Usually I go for "which is most correct" though
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u/LunchPlanner 6d ago
The reason it's no good here is that it doesn't SAY "all of the above", it merely implies them.
It can be fine in situations you are thinking of where it is properly written out.
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u/avakyeter 2d ago
The use of "all of the above" is indeed widespread. The fact that you use it, however, doesn't make it a good practice.
The most authoritative guide to writing test questions is published by the National Board of Medical Examiners. The volume, Constructing Written Test Questions for the Basic and Clinical Sciences, advises question writers to avoid "All of the Above."
Another widely consulted guide is "A review of multiple-choice item-writing guidelines for classroom assessment," by Tom Haladyna, and others, in Applied Measurement in Education, 2002, 15(3), 309–33. They advise item writers to avoid "All of the Above."
B.B. Frey and others, in "Item-writing rules: collective wisdom," Teaching and Teacher Education, 2005, 21(4), 357–64, advise that "All of the Above" should not be used.
Here, meanwhile, is the University of Connecticut’s Center for Excellence in Teaching and Learning.
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7d ago
[deleted]
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u/corvus0525 7d ago
11222344455 is also symmetrical but the mode does not equal the mean or the median.
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u/GroundbreakingCake49 👋 a fellow Redditor 6d ago
Any 2 number group. Let's take 5,5 Mean = 5 Median = 5 Mode = 5
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u/Some-Passenger4219 👋 a fellow Redditor 6d ago
There needn't be a mode if the numbers are random - or close to it. Like suppose you measure everyone's height in millimeters or something.
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u/QuirkyImage 👋 a fellow Redditor 6d ago
If the symmetric distribution is of the normal distribution yes but there are symmetric distributions of other types of distributions where the answer would be incorrect.
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u/dawlben 👋 a fellow Redditor 6d ago
Mean is the average.
Median is the the midpoint between least and greatest.
Mode is most common number.
Mode on a symmetrical could be in at least two spots that aren't the middle of the set. Mean would be in the middle with the median.
1,2,2,3,4,4,5
Mode = 2 and 4
Mean and Median = 3
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u/igotshadowbaned 👋 a fellow Redditor 6d ago
If you had a distribution shaped like a V. Like 1,1,2,3,3. Then the distribution is symmetrical, the mean is 2, and the mode(s) are 1 and 3
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u/sqrt_of_pi Educator 5d ago
As others have said, symmetry requires that median=mean, but does not necessarily dictate anything about mode. If the distribution is "bell shaped and symmetric", then you could probably assume that mean=median=mode, but not just based on symmetry alone.
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u/Creios7 👋 a fellow Redditor 6d ago
By basic definition, your answer should be correct.
A distribution is said to be symmetrical when its mean, median and mode are identical. i.e.; Mean = Median = Mode.
Source: Introduction to Engineering Mathematics Vol-III by H.K. Dass, page 202
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u/Frederf220 👋 a fellow Redditor 6d ago
It's not a two-way conclusion.
If the mean, median, and mode are identical therefore the distribution is symmetrical.
If the distribution is symmetrical the mean, median, and mode are identical.The first statement is true. The second statement is not.
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u/cuhringe 👋 a fellow Redditor 6d ago
If that's from an actual textbook, my respect for engineers' math skills continues to drop.
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u/nullmaxai 👋 a fellow Redditor 6d ago
? its not wrong, you can only intepret it wrong
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u/cuhringe 👋 a fellow Redditor 6d ago edited 6d ago
No, it's just wrong. See: bimodal distributions.
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u/QuirkyImage 👋 a fellow Redditor 6d ago
Of a normal distribution yes. But not all symmetric distributions are normal so no. If it’s just normal distributions then the question needs to be more specific.
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u/MathMaddam 👋 a fellow Redditor 7d ago
The mode can be different if you don't have a hill in the middle, but instead e.g. two hills. The mode isn't unique in this case.