If two data sets have the same range:
a) the distances from the smallest to largest observations in both sets will be the same
b) the smallest and largest observations are the same in both sets
c) both sets will have the same mean
d) both sets will have the same interquartile range
e) none of these
- Which of the following summary measures is affected least by outliers?
a) The median
b) The variance
c) The range
d) The mean
e) None of these
- 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 :
- Answer: a) the distances from the smallest to largest observations in both sets will be the same Explanation: The range of a data set is defined as the difference between the largest and smallest observations. If two data sets have the same range, it means that the difference between their largest and smallest values is identical. However, this does not imply that the smallest or largest values in each set are the same, nor does it suggest anything about the mean or interquartile range (IQR). The interquartile range (IQR) measures the spread of the middle 50% of the data, so it could differ even with the same range. Therefore, option a is correct, as it specifically addresses the equality of the distances between the smallest and largest observations.
- Answer: a) The median Explanation: Outliers are extreme values that differ significantly from other observations in a data set. They can distort many summary measures. The median, however, is less sensitive to outliers compared to other measures. This is because the median is the middle value when the data is ordered, and it is only affected by extreme values if those values affect the middle of the data distribution. In contrast, the mean is highly sensitive to outliers because it incorporates all values in the data, including the extreme ones. The variance and range are both also sensitive to outliers, as they depend on the spread and the maximum or minimum values. Therefore, the median is the best summary measure that is least affected by outliers.
- Answer: e) None of these Explanation: Measures of variability assess the spread or dispersion within a data set. The range is the difference between the maximum and minimum values, which measures the overall spread of the data. The variance measures the average squared deviation of each data point from the mean, indicating how spread out the data is. The interquartile range (IQR) focuses on the middle 50% of the data, measuring the spread between the first and third quartiles. The standard deviation is the square root of the variance, providing a measure of variability in the same units as the original data. All of the options provided (range, variance, IQR, and standard deviation) are indeed measures of variability. Thus, none of these options is incorrect in this context.