7.Which of the following measures of the central tendency suits the data best if the objective is to assess the distribution of values? a. Arithmetic mean b. Mode c. Median d. Kurtosis
The Correct Answer and Explanation is :
Correct Answer: c. Median
Explanation:
The median is the most suitable measure of central tendency when the objective is to assess the distribution of values, especially in data that is skewed or contains outliers. Here’s why:
- Definition of Median:
The median is the middle value of a dataset when it is ordered from smallest to largest. If there is an even number of observations, the median is the average of the two middle values. - Robustness to Outliers:
The median is not affected by extremely high or low values (outliers) in the data. In contrast, the arithmetic mean can be heavily skewed by such values, leading to an inaccurate representation of the central tendency. - Applicability to Skewed Data:
For skewed distributions (e.g., income, house prices), the median provides a better central value than the mean. The mean can be pulled toward the tail of the distribution, but the median remains centered in the dataset. - Distribution Assessment:
The median splits the dataset into two equal halves, offering a clear perspective on the distribution of values. By comparing the median to other measures, such as the mean, one can infer skewness. For example:
- If the mean > median, the distribution is positively skewed.
- If the mean < median, the distribution is negatively skewed.
- Why Not Other Measures:
- Arithmetic Mean: Affected by outliers and skewness, making it less suitable for assessing the distribution.
- Mode: Indicates the most frequently occurring value but does not give insight into the overall distribution.
- Kurtosis: Describes the shape (peakedness) of the distribution rather than central tendency.
Thus, the median is preferred when the goal is to assess the distribution of values accurately, particularly in the presence of skewness or outliers.