Statistics - 3.4

Resistance

The correct answer is resistance. A numerical summary of data is said to be resistant if extreme values​ (very large or​ small) relative to the data do not affect its value substantially. Notice that for this data set the standard deviation is not resistant to extreme​ observations, but the interquartile range is resistant.

Z-score

The z-sore represents the distance that a data value is from the mean in terms of the number of standard deviations. The z-score is unitless. It has mean 0 and standard deviation 1.

The interquartile range

The interquartile range is the difference between the third and first quartiles. It is the range of the middle 50% of the observations in the data set.

The​ _______ represents the number of standard deviations an observation is from the mean.

Z-score

Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile​ range?

The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation. The interquartile​ range, IQR, is the range of the middle​ 50% of the observations in a data set. That​ is, the IQR is the difference between the first and third quartiles. The interquartile range is not affected by extreme values.​ Therefore, when the distribution of data is highly skewed or contains extreme​ observations, it is best to use the interquartile range as the measure of dispersion because it is resistant. The standard deviation describes how​ far, on​ average, each observation is from the mean. It is affected by extreme​ values, but the advantage that it has over the interquartile range is that it uses all the observations in its computation.