Final answer:
The Correct option is 1). The acceptable range for determining if variances are significant is defined by the standard deviation. This measure of spread indicates how far data values are from the mean, with smaller standard deviations indicating less variation and larger ones indicating more.
Step-by-step explanation:
The acceptable range is a term used to determine if variances within a set of data are significant. The standard way to define this range is by standard deviation, which is a measure of the overall variation or spread in a data set. The standard deviation tells us how far data values are from the mean, with a small standard deviation indicating that the data points are close to the mean, and a larger one indicating that the data points are more spread out.
When assessing whether a particular data value is within an acceptable range, one compares it to the standard deviation. A commonly used rule of thumb in statistics is Chebyshev's Rule, which tells us that at least 75 percent of the data is within two standard deviations of the mean. For a normal distribution, also known as a bell-shaped distribution, 68 percent of the data lies within one standard deviation of the mean, 95 percent within two standard deviations, and 99.7 percent within three standard deviations, according to the empirical rule.