When data has a long tail on the right side.

by

When data has a long tail on the right side, it is said to be “skewed left.” True False

Final Answer:

The statement is false; when data has a long tail on the right side, it is skewed right, not left. Right skewness means most data points are on the left with the tail extending to the right due to high values. This understanding is important for proper data analysis and interpretation.

Examples & Evidence:

The statement is false. When data exhibits a long tail on the right side, it is said to be skewed right, also known as positively skewed. In this situation, most of the data points are concentrated on the left side of the distribution, while the tail extends to the right due to a few exceptionally high values.

Explanation of Skewness:

Skewness Definition: Skewness measures the asymmetry of a distribution.

Right Skewed (Positive Skew):

  • In a right-skewed distribution, the tail stretches out longer towards the right.
  • This results from a few high outliers that pull the mean to the right of the median.
  • The majority of data points are to the left of the mean.

Left Skewed (Negative Skew):

  • If data were skewed left, the tail would be longer on the left side.
  • Here, the mean would be less than the median, suggesting more low outliers.

Visualization:

Imagine a graph where the bulk of the values are clustered at lower numbers with just a few higher numbers extending into the right. That’s the appearance of a right-skewed distribution.

Importance of Understanding Skewness:

  • Knowing whether a distribution is skewed helps in proper data analysis and interpretation, particularly when identifying averages like the mean, median, and mode.
  • It also impacts statistical conclusions drawn from the data.

Explanation:

For example, if test scores in a class predominantly fall between 60 and 80 but a few students score over 100, the distribution of scores would be right-skewed. Conversely, if most students scored highly but a few failed, the distribution might be left-skewed.

Statistical definitions and examples of skewness indicate that right skewness is defined by a longer tail on the right side of the distribution, clearly differentiating it from left skewness.

More Answers:

Leave a Comment