3-100
Matthews, Young and Associates, a Chapel Hill consulting firm, has these records indicating the number of days each of its ten staff consultants billed last year:
212 320 230 210 229 231 219 221 222
a)Without computing the value of any of these measures, which of them would you guess would give you more information about this distribution: range or standard deviation?
b) Considering the difficulty and time of computing each of the measures you reviewed in part (c), which one would you suggest is better?
(d) What will cause you to change your mind about your choice?
To determine which measure would provide more information about the distribution, let's examine the concepts of range and standard deviation.
a) Range: Range is the difference between the maximum and minimum values in a dataset. It provides a measure of the spread or dispersion of the data. For the given scenario, the range would be calculated by subtracting the minimum (210) from the maximum (320), resulting in a range of 320 - 210 = 110.
Standard Deviation: Standard deviation measures the average deviation of values from the mean (average) of a dataset. It indicates how much the values vary from the mean. Calculating the standard deviation requires more computation, as it involves multiple steps such as finding the mean, calculating the deviations from the mean, squaring the deviations, averaging the squared deviations, and taking the square root.
Considering the above explanations, the standard deviation would provide more information about the distribution than the range. This is because the standard deviation takes into account the dispersion or variability of all the values, rather than just the difference between the maximum and minimum.
b) Given the difficulty and time involved in computing the measures, it is suggested that range is a simpler measure to compute compared to standard deviation. Calculating the range only requires finding the maximum and minimum values in the dataset, whereas calculating the standard deviation involves multiple steps and computations.
d) One might change their mind about their choice based on the specific characteristics of the dataset. If the dataset has outliers or extreme values that significantly impact the range, it may lead to a skewed understanding of the variability in the data. In such cases, the standard deviation might provide a more accurate representation of the dispersion. Additionally, if the dataset is normally distributed, the standard deviation would provide a better measure of how closely the values cluster around the mean.
Overall, the choice between range and standard deviation depends on the specific requirements of the analysis and the characteristics of the dataset being analyzed.