Chapter 3 Describing Data Using Numerical Measures Flashcards
Parameter
A measure computed from the entire population. As long as the population does not change, the value of the parameter will not change.
Statistic
A measure computed from a sample that has been selected from a population. The value of the statistic will depend on which sample is selected.
Mean
A numerical measure of the center of a set of quantitative measures computed by dividing the sum of the values by the number of values in the data.
Population Mean
The average for all values in the population computed by the dividing the sum of all values by the population size.
Sample Mean
The average for all values in the sample computed by dividing the sum of all sample values by the sample size.
Median
The median is a center value that divides a data array into two halves. We use “U” to denote the population median and “M” to denote the sample median.
Data Array
Data that have been arranged in numerical order.
Symmetric Data
Data sets whose values are evenly spread around the center. For symmetric data, the mean and median are equal.
Skewed Data
Data sets that are not symmetric. For skewed data, the mean will be larger or smaller than the median.
Right-Skewed Data
A data distribution is right skewed if the mean for the data is larger than the median.
Left-Skewed Data
A data distribution is left skewed if the mean for the data is smaller than the median.
Mode
The mode is the value in a data set that occurs most frequently
Weighted Mean
The mean value of data values that have been weighted according to their relative importance.
Percentiles
The Pth percentile in a data array is a value that divides the data set into two parts. The lower segment contains at least P% and the upper segment contains at least (100-P)% of the data. The 50th percentile is the median.
Quartiles
Quartiles in a data array are those values that divide the data set into four equal-sized groups. The median corresponds to the second quartile.
Box and Whisker Plot
A graph that is composed of two parts: a box and the whiskers. The box has a width that ranges from the first quartile (Q1) to the third quartile (Q3). A vertical line through the box is placed at the median. Limits are located at a value that is 1.5 times the difference between Q1 and Q3 below Q1 and above Q3. The whiskers extend to the left to the lowest value within the limits and to the right to the highest value within the limits.
Variation
A set of data exhibits variation if all the data are not the same value.
Range
The range is a measure of variation that is computed by finding the difference between the maximum and minimum values in a data set.
Interquartile Range
The interquartile range is a measure of variation that is determined by computing the difference between the third and first quartiles.
Variance
The population variance is the average of the squared distances of the data values from the mean.
Standard Deviation
The standard deviation is the positive square root of the variance.
Coefficient of Variation
The ratio of the standard deviation to the mean expressed as a percentage. The coefficient of variation is used to measure variation relative to the mean.
