How is this graph NEGATIVELY SKEWED

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In summary, the conversation discusses the concept of a negatively skewed graph and how it is identified by a tail in the low x-values. The individual is having difficulty seeing the negative skew in the given graph and asks for clarification. They also mention the relationship between the tail and the median/mode, stating that for a negative skew, the mean is less than the median and mode. The conversation ends with the book's explanation that the mean will lie on the longer side of the graph.
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jsmith613
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Homework Statement


http://www.thestudentroom.co.uk/attachment.php?attachmentid=103146&d=1306479703

Look at question 3(d)
and the graph for question 3
how is this graph NEGATIVELY SKEWED

Homework Equations


The Attempt at a Solution


I know that a -ve skew has a tail in the low x-values but I find it difficult to see that here :(

(I am not sure what further attempt I can give, I have said everything I know about shapes of skewed curves I just cannot see why it is -ve. I was hoping someone could help me with this!)
 
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  • #2


Look at the answer to part c, a = 5.

So the left tail is 3 units long and the right tail is 2 units long
 
  • #3


rollcast said:
Look at the answer to part c, a = 5.

So the left tail is 3 units long and the right tail is 2 units long

I always though the tail was a flat bit? how does the tail relate to the median / mode
is it as follows:
the mode is assumed to be the middle of the graph
if the a<x<mode is greater than mode<x<b for a graph a<x<b then it is negative skew
if a<x<mode is less than mode<x<b then the graph for a<x<b is +ive skew?
 
  • #4


Sorry I was in the wrong part of my book for the answer, ok not much help but my book says

Negative skew = Mean < Median < Mode.

Positive skew = Mean > Median > Mode.
 
  • #5


Then you can deduce that because the area of both sides of the mode is the same, then the mean will lie on the longer side.
 
  • #6


oh I see
ok
thanks
 

FAQ: How is this graph NEGATIVELY SKEWED

What does "negatively skewed" mean in a graph?

Negatively skewed refers to the shape of a graph in which the data is clustered towards the higher end of the x-axis and tapers off towards the lower end. This means that the majority of the data points are towards the left side of the graph and there are fewer data points towards the right side.

How can you identify a negative skew in a graph?

A negative skew can be identified by looking at the shape of the graph. If the majority of the data points are on the left side of the graph and there is a long tail on the right side, this indicates a negative skew. Another way to identify a negative skew is by calculating the skewness coefficient, which is a measure of the asymmetry of the data distribution.

What causes a graph to be negatively skewed?

A graph can be negatively skewed when there are outliers or extreme values on the higher end of the data. This pulls the mean towards the higher end and causes the tail to extend towards the lower end, resulting in a negative skew. It can also occur when the data is naturally distributed in a way that the majority of the values are on the lower end.

How does a negative skew affect the interpretation of the data?

A negative skew can affect the interpretation of the data by making it appear that the data is more clustered towards the lower end than it actually is. This can lead to an overestimation of the mean and an underestimation of the variability in the data. It is important to take the skewness of a graph into account when analyzing and interpreting data.

Can a negatively skewed graph still be considered normal?

Yes, a negatively skewed graph can still be considered normal if the data does not significantly deviate from a normal distribution. This means that the data points are still clustered around the mean, and the majority of the data falls within one standard deviation of the mean. However, it is important to note the negative skew when analyzing and interpreting the data.

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