For data skewed to the left, the skewness is _. Option
A between 0 and .5
B less than 1
C negative
D positive
The correct answer and explanation is:
The correct answer is Option C: negative.
Explanation:
Skewness refers to the measure of the asymmetry or distortion in the distribution of data. It shows whether the data is balanced or has a tail on one side. In statistical terms, skewness can be categorized as positive, negative, or near zero.
When data is skewed to the left, also known as left-skewed or negatively skewed, it means that the tail of the distribution extends more to the left (towards the lower values), while most of the data is concentrated towards the right (the higher values). This results in a negative skewness value, typically between -0.5 and -1. A higher negative value would indicate a stronger skewness.
Mathematically, skewness is calculated using the third standardized moment, and the formula generally looks at the third power of the deviations from the mean. When the left tail is longer or more pronounced than the right tail, the value for skewness is negative. This is why the correct answer to this question is negative.
In contrast:
- Positive skewness (right-skewed) occurs when the tail is on the right side of the distribution, which means the majority of the data values are on the lower end.
- Zero or near zero skewness would indicate a symmetric distribution, such as a normal distribution.
Understanding skewness helps to interpret data better because it provides insights into the shape and spread of the data. A negative skewness indicates the presence of outliers on the lower end of the data, and understanding this can help in making better decisions, particularly in fields like finance, economics, and engineering.