Fdfd
SKEWNESS
All about Skewness: • Aim • Definition • Types of Skewness • Measure of Skewness • Example A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis. Measure of Dispersion tells us about the variation of the data set. Skewness tells us about the direction of variation of the data set.
Definition:
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
Types of Skewness:
Teacher expects most of the students get good marks. If it happens, then the cure looks like the normal curve bellow:
But for some reasons (e. g., lazy students, not understanding the lectures, not attentive etc.) it is not happening. So we get another two curves.
Positive Skewness
Negative Skewness
The first one is known as positively skewed and the second one is known as negatively skewed curve.
Positive vs. Negative Skewness
These graphs illustrate the notion of skewness. The one on the left is positively skewed. The one on the right is negatively skewed.
Measure of Skewness:
1. Karl Pearson coefficient of Skewness Sk = 3(mean - median) / Standard Deviation. = 3(X –Me) / S 2. The skewness of a random variable X is denoted or skew(X). It is defined as:
where and are the mean and standard deviation of X. Interpretation: 1. If Sk = 0, then the frequency distribution is normal and symmetrical. 2. If Sk 0, then the frequency distribution is positively skewed. 3. If Sk 0, then the frequency distribution is negatively skewed.
Example:
The length of stay on the cancer floor of Apolo Hospital were organized into a frequency distribution. The mean length of stay was 28 days, the medial 25 days and modal length is 23 days. The standard deviation was computed to be 4.2 days. Is the distribution symmetrical, or skewed?
All about Skewness: • Aim • Definition • Types of Skewness • Measure of Skewness • Example A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis. Measure of Dispersion tells us about the variation of the data set. Skewness tells us about the direction of variation of the data set.
Definition:
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
Types of Skewness:
Teacher expects most of the students get good marks. If it happens, then the cure looks like the normal curve bellow:
But for some reasons (e. g., lazy students, not understanding the lectures, not attentive etc.) it is not happening. So we get another two curves.
Positive Skewness
Negative Skewness
The first one is known as positively skewed and the second one is known as negatively skewed curve.
Positive vs. Negative Skewness
These graphs illustrate the notion of skewness. The one on the left is positively skewed. The one on the right is negatively skewed.
Measure of Skewness:
1. Karl Pearson coefficient of Skewness Sk = 3(mean - median) / Standard Deviation. = 3(X –Me) / S 2. The skewness of a random variable X is denoted or skew(X). It is defined as:
where and are the mean and standard deviation of X. Interpretation: 1. If Sk = 0, then the frequency distribution is normal and symmetrical. 2. If Sk 0, then the frequency distribution is positively skewed. 3. If Sk 0, then the frequency distribution is negatively skewed.
Example:
The length of stay on the cancer floor of Apolo Hospital were organized into a frequency distribution. The mean length of stay was 28 days, the medial 25 days and modal length is 23 days. The standard deviation was computed to be 4.2 days. Is the distribution symmetrical, or skewed?