Skewed Distribution
This page is based on Skewed distribution which is an important topic of statistics
. Skewed distribution , mean and median defintion is given briefly at first and then further examples are provided for you to avail proper statistics help.
Skewed distribution:
Skewed Distribution is defined as an asymmetrical in scattering, as skewness which means unevenness of frequencies across scores. Skewed distribution can be classified as negatively skewed or positively skewed.
Mean:
It is shortly defined as the average of the given numbers.
Median:
It is the middle value of the given data set to be arranged in either ascending or descending order.
Negatively Skewed Distribution
Skewness is a determination of the irregularity of the probability distribution of a real-valued random variable. The value of skewness can be positive or negative, or even it may be not defined.
Negative skewed distribution:
A negative skew shows that the end on the left side of probability density function is higher than the right side .The bulk of the values lie to the right of the mean including the median.
negatively skewed distribution
where A indicates mean
B indicates median and
C indicates mode.
Positively Skewed Distribution
Here is explained on positively Skewed distribution. A positive skew shows that the end on the right side is higher than the left side and the more values lie to the left of the mean. A zero value shows that the values are relatively equally distributed on both sides of the mean, usually imply a symmetric distribution.
poisitively skewed distribution
where A indicates mean
B indicates median and
C indicates mode.
The following figure shows that the frequency distribution is skewed normally.
frequency distribution
The following bar diagram shows that the frequency distribution is skewed left.
frequency distribution
The following bar diagram shows that the frequency distribution is skewed right.
frequency distribution
If there is a symmetric distribution then we have mean = median.So there is no skewness in the distribution.
Skewed Distribution - Examples
Below are solved examples on Skewed distribution for your better understanding:
Example 1:
Suppose if a data is set with a left-skewed distribution. Explain that which will be larger mean or median?
Explanation:
Because of the higher attention of larger values in a left-skewed distribution the mean would be larger than the median. Though, if there were a important number of very smaller values in the distribution, they would may affect the mean and the median and hence cause mean to be likely higher.
Example 2:
A government account looked at the sum rented for college by the students who graduated in 2007 and had taken out for the student loans. The mean amount was about $ 16, 571 and the standard deviation was s = $11,114. The quartile Q1 = $8103,Median M = $14,910, and the quartile Q3 = $23,009.
Compare the mean and the median M and compare the distances of Q 1 and Q 3 from the median. Explain why both comparisons imply that the distribution is right-skewed.
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Explanation:
We know that the mean is greater than the median, when the distribution is right-skewed. The distance from Q1 to M ($6807) which is shorter than the distance from M to Q3 ($8099). This also happens when there is right-skewed distribution..
by: johnharmer
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