Mode
Nobody invented skewed distributions! There are more distributions that are skewed than are symmetrical, and they were discovered as various distribution functions were discovered.
No.
A normal distribution is not skewed. Skewness is a measure of how the distribution has been pulled away from the normal.A feature of a distribution is the extent to which it is symmetric.A perfectly normal curve is symmetric - both sides of the distribution would exactly correspond if the figure was folded across its median point.It is said to be skewed if the distribution is lop-sided.The word, skew, comes from derivations associated with avoiding, running away, turning away from the norm.So skewed to the right, or positively skewed, can be thought of as grabbing the positive end of the bell curve and dragging it to the right, or positive, direction to give it a long tail in the positive direction, with most of the data still concentrated on the left.Then skewed to the left, or negatively skewed, can be thought of as grabbing the negative end of the bell curve and dragging it to the left, or negative, direction to give it a long tail in the negative direction, with most of the data still bunched together on the right.Warning: A number of textbooks are not correct in their use of the term 'skew' in relation to skewed distributions, especially when describing 'skewed to the right' or 'skewed to the left'.
It is not at all skewed. As to oddly shaped, it depends on your expectations.
i) Since Mean<Median the distribution is negatively skewed ii) Since Mean>Median the distribution is positively skewed iii) Median>Mode the distribution is positively skewed iv) Median<Mode the distribution is negatively skewed
Not necessarily.
If the distribution is positively skewed , then the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency (If it is a uni-modal distribution). If the distribution is negatively skewed then mean will always be the lowest estimate of central tendency and the mode will be the highest estimate of central tendency. In both positive and negative skewed distribution the median will always be between the mean and the mode. If a distribution is less symmetrical and more skewed, you are better of using the median over the mean.
In general the distribution of F-ratio means what
As the mean is greater than the median it will be positively skewed (skewed to the right), and if the median is larger than the mean it will be negatively skewed (skewed to the left)
When the data distribution is negatively skewed.
If most the population has many high scores, the distribution is negatively skewed. If most have many low scores, it is positively skewed
Mode
3median - 2mean = mode
A distribution or set of observations is said to be skewed left or negatively skewed if it has a longer "tail" of numbers on the left. The mass of the distribution is more towards the right of the figure rather than the middle.
If the distribution is positively skewed distribution, the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency. This is true if we assume the distribution has a single mode.
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