ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: PopcornTime on December 11, 2017, 08:13:45 pm
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1. If the level of mathematical ability, lets say represented on a box plot, is negatively skewed, what would this suggest about the data? What about if the box plot was positively skewed? Would this mean the mathematical ability represented by the positively skewed distribution is lower than the negatively skewed distribution?
Thanks!
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1. If the level of mathematical ability, lets say represented on a box plot, is negatively skewed, what would this suggest about the data? What about if the box plot was positively skewed? Would this mean the mathematical ability represented by the positively skewed distribution is lower than the negatively skewed distribution?
Thanks!
If something is positively skewed, then the scores will fall towards the lower side of the scale and there are very few higher scores.
If something is negatively skewed, then the scores will fall towards the higher side of the scale and there are very few low scores.
For example, a poorly completed exam will be positively skewed, as there will be very few higher scores, and an exam that is very well done overall will be negatively skewed, as there will be more scores towards the higher side, meaning very few low scores. \
So yes, you're correct, the mathematical ability represented by the positively skewed distribution will be lower than the negatively skewed distribution.
Hope this helps :)
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If something is positively skewed, then the scores will fall towards the lower side of the scale and there are very few higher scores.
If something is negatively skewed, then the scores will fall towards the higher side of the scale and there are very few low scores.
For example, a poorly completed exam will be positively skewed, as there will be very few higher scores, and an exam that is very well done overall will be negatively skewed, as there will be more scores towards the higher side, meaning very few low scores. \
So yes, you're correct, the mathematical ability represented by the positively skewed distribution will be lower than the negatively skewed distribution.
Hope this helps :)
Thanks!
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Hi!
Just thought I'd add onto snowisawesome's answers with a few diagrams. Skewness is basically used in Futher Math as a qualitative descriptor of the asymmetrical nature of a distribution. Here's a diagram showing how positive and negative skew appear on a probability distribution function.
(https://qph.ec.quoracdn.net/main-qimg-5fc78a3359ad31c9c457dd4825813185-c)
Although the naming convention may seem counter-intuitive at first, as it does not refer to the direction in which the curve is 'leaning' towards, it is easier to remember if you instead remember that it describes the side with a stretched tail. For example, a positively skewed distribution will have a longer tail towards the more positive end. Also take note of the relative magnitude of the mean, median and mode for each type of skew.
As you mentioned, skew can also be exhibited in box plots.
(http://datapigtechnologies.com/blog/wp-content/uploads/2014/11/111714_1527_MethodsofMe3.png)
So yes, as snowisawesome already said, your example is correct, as a negative skew results from a larger amount of data points with a higher value, resulting in an increased mean, whereas the positively skewed set has a much lower mean due to a large amount of data points with lower values. Hopefully these diagrams help it make a little more sense.
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yep definitely does!
Hi!
Just thought I'd add onto snowisawesome's answers with a few diagrams. Skewness is basically used in Futher Math as a qualitative descriptor of the asymmetrical nature of a distribution. Here's a diagram showing how positive and negative skew appear on a probability distribution function.
(https://qph.ec.quoracdn.net/main-qimg-5fc78a3359ad31c9c457dd4825813185-c)
Although the naming convention may seem counter-intuitive at first, as it does not refer to the direction in which the curve is 'leaning' towards, it is easier to remember if you instead remember that it describes the side with a stretched tail. For example, a positively skewed distribution will have a longer tail towards the more positive end. Also take note of the relative magnitude of the mean, median and mode for each type of skew.
As you mentioned, skew can also be exhibited in box plots.
(http://datapigtechnologies.com/blog/wp-content/uploads/2014/11/111714_1527_MethodsofMe3.png)
So yes, as snowisawesome already said, your example is correct, as a negative skew results from a larger amount of data points with a higher value, resulting in an increased mean, whereas the positively skewed set has a much lower mean due to a large amount of data points with lower values. Hopefully these diagrams help it make a little more sense.