Frequency distributions can assume many shapes. The three
most important shapes are positively skewed, symmetric, and negatively skewed.
In a positively or skewed right skewed distribution, the majority of the data values fall to the left of the mean and cluster at the lower end of the distribution; the “tail” is to the right. Also, the mean is to the right of the median, and the mode is to the left of the median.
For example, if an instructor gave an examination and most of the students did poorly; their scores would tend to cluster on the left side of the distribution. A few high scores would constitute the tail of the distribution, which would be on the right side. Another example of a positively skewed distribution is the incomes of the population of the United States. Most of the incomes cluster about the low end of the distribution; those with high incomes are in the minority and are in the tail at the right of the distribution.
In a symmetric distribution, the data values are evenly distributed on both sides of the mean. In addition, when the distribution is unimodal, the mean, the median, and the mode are the same and are at the center of the distribution. Examples of symmetric distributions are IQ scores and heights of adult males.
When the majority of the data values fall to the right of the mean and cluster at the upper end of the distribution, with the tail to the left, the distribution is said to be negatively skewed or left-skewed. Also, the mean is to the left of the median, and the mode is to the right of the median. As an example, a negatively skewed distribution results if the majority of students score very high on an instructor’s examination. These scores will tend to cluster to the right of the distribution.
When a distribution is extremely skewed, the value of the mean will be pulled toward the tail, but the majority of the data values will be greater than the mean or less than the mean (depending on which way the data are skewed); hence, the median rather than the mean is more appropriate measure of central tendency. An extremely skewed distribution can also affect other statistics.
by: Marie Louissie Ynez U. Lavega
In a positively or skewed right skewed distribution, the majority of the data values fall to the left of the mean and cluster at the lower end of the distribution; the “tail” is to the right. Also, the mean is to the right of the median, and the mode is to the left of the median.
For example, if an instructor gave an examination and most of the students did poorly; their scores would tend to cluster on the left side of the distribution. A few high scores would constitute the tail of the distribution, which would be on the right side. Another example of a positively skewed distribution is the incomes of the population of the United States. Most of the incomes cluster about the low end of the distribution; those with high incomes are in the minority and are in the tail at the right of the distribution.
In a symmetric distribution, the data values are evenly distributed on both sides of the mean. In addition, when the distribution is unimodal, the mean, the median, and the mode are the same and are at the center of the distribution. Examples of symmetric distributions are IQ scores and heights of adult males.
When the majority of the data values fall to the right of the mean and cluster at the upper end of the distribution, with the tail to the left, the distribution is said to be negatively skewed or left-skewed. Also, the mean is to the left of the median, and the mode is to the right of the median. As an example, a negatively skewed distribution results if the majority of students score very high on an instructor’s examination. These scores will tend to cluster to the right of the distribution.
When a distribution is extremely skewed, the value of the mean will be pulled toward the tail, but the majority of the data values will be greater than the mean or less than the mean (depending on which way the data are skewed); hence, the median rather than the mean is more appropriate measure of central tendency. An extremely skewed distribution can also affect other statistics.
by: Marie Louissie Ynez U. Lavega
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