3.1

what does it mean if a statistic is resistant?

Extreme values (very large or small) relative to the data do not affect its value substantially

True or False: When an observation that is much larger than the rest of the data is added to a data set, the value of the median will increase substantially

False

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. when data are either skewed left or skewed right, there are extremes values in the tail, which tend to pull the mean in the direction of the tail. if the distribution of the data is skewed right, there are large observations in the right tail. these observations tend to increase the value of the mean, while having little effect on the median.

median of a variable

is the value that lies in the middle of the data when arranged in ascending order. We use M to represent the median.

True or False: A data set will always have exactly one mode

False. A mode of a variable is the most frequent observation of the variable that occurs in the data set. To compute the mode, tally the number of observations that occur for each data value. The data value that occurs most often is the mode. A set of data can have no mode, one mode, or more than one mode. If no observation occurs more than once, the data have no mode.

arithmetic mean

Is computed by adding all the values of the variable in the data set and dividing by the number of observations. generally referred to as the mean.

For a distribution that is skewed left, which of the following is true?

Mean<Median

For a distribution that is symmetric, which of the following is true?

Mean=Median

For a distribution that is skewed right, which of the following is true?

Mean>Median

population arithmetic mean

computed using all the individuals in a population (parameter)

sample arithmetic mean (x-bar)

computed using sample data. the sample mean is a statistic.

why is the median resistant, but the mean is not?

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. The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. For​ example, in​ skewed-right distributions, there are large observations in the right tail. These observations increase the value of the​ mean, but have little effect on the median. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.