Which of the following is not a measure of variability? a) The range b) The variance c) The interquartile range d) The standard deviation e) None of these
The correct answer and explanation is:
Correct Answer: e) None of these
All the options listed—range, variance, interquartile range, and standard deviation—are valid measures of variability. Therefore, the correct answer is “none of these.”
Variability refers to the extent to which data points in a statistical distribution or data set diverge from the average or mean. It gives insight into the spread or dispersion of the data. Understanding variability helps interpret how consistent or inconsistent the data is.
The range is the simplest measure of variability. It is calculated as the difference between the largest and smallest values in a data set. Although easy to compute, it is very sensitive to outliers and does not reflect the distribution of values between the extremes.
The variance measures the average squared deviation of each data point from the mean. It is a key concept in statistics and provides a more comprehensive understanding of data spread than the range. Variance is expressed in the squared units of the data, which makes it less interpretable in practical terms.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It captures the spread of the middle 50 percent of the data. Because it ignores extreme values, the IQR is less affected by outliers and is especially useful for skewed distributions.
The standard deviation is the square root of the variance. It measures how much values typically differ from the mean. Like variance, it provides a detailed view of variability, but it is more interpretable because it is in the same units as the original data.
Since all the options provided are legitimate measures of variability, none of them can be considered an incorrect choice. Thus, the correct response is e) None of these.