Module 02 Quantitative Data

Essential Statistics

Frequency distribution or frequency table

shows how data are partitioned among several categories (or classes) by listing the categories along with the num-ber (frequency) of data values in each of them.

Lower Class Limits

are the smallest numbers that can belong to each of the differ-ent classes.

Upper Class Limits

are the largest numbers that can belong to each of the different classes.

Class Boundaries

are the numbers used to separate the classes, but without the gaps created by class limits

Class Midpoints

are the values in the middle of the classes. Table 2-2 has class midpoints of 7, 22, 37, 52, 67, 82, and 97. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2.

Class Width

is the difference between two consecutive lower class limits (or two con-secutive lower class boundaries) in a frequency distribution. Table 2-2 uses a class width of 15. (The first two lower class limits are 0 and 15, and their difference is 15.)

Histogram

is a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values.

Dotplot

Consists of a graph of quantitative data in which each data value is plotted as a point (or dot) above a horizontal scale of values

Stemplot (or steam and leaf plot)

represents quantitative data by seperating each value into two parts: the stem (such as leftmost digit) and the leaf (such as the rightmost digit)

Time series graph

is a graph of time series data, which are quantitative data that have been collected at different points in time, such as monthly or yearly

Bar Graph

uses bars of equal width to show frequencies of categories of categorical or qualitative data

Pareto Chart

is a bar graph for categorical data, with the added stipulation that the bars are arranged in descending order according to frequencies, so the bars decrease in height from left to right.

Pie Chart

is a very common graph that depicts categorical data as slices of a circle, in which the size of each slice is proportional to the frequency count for the category.

Frequency Polygon

uses line segments connected to points located directly above class midpoint values

Relative frequency polygon

which uses relative frequencies (proportions or percentages) for the vertical scale

Nonzero Axis

Always examine a graph carefully to see whether a vertical axis begins at some point other than zero so that differences are exaggerated

Pictographs

When examining data depicted with a pictograph, determine whether the graph is misleading because objects of area or volume are used to depict amounts that are actually one-dimensional. (Histogram and bar charts represent one-dimensional data with two-dimensional bars, but they use bars with the same width so that the graph is not misleading.)

Measure of Center

is a value at the center or middle of a data set

Mean or arithmetic mean

of a set of data is the measure of center found by adding all of the data values and dividing the total by the number of data values

Resistant

A statistic is _________, if the presence of extreme values (outliers) does not cause it to change very much

Median

of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude.

Mode

of a data set is the value that occurs with the greatest frequency

Midrange

of a data set is the measure of center that is the value midway between the maximum and minimum values in the original data set. It is found by adding the maximum data value to the minimum data value and then dividing the sum by 2 

Range

of a set of data is the difference the maximum data value and the minimum data value

Standard Deviation

of a set of sample values, denoted by s, is a measure of how much data values deviate away from the mean.

Variance

of a set of values is a measure of variation equal to the square of the standard deviation

Coefficient of variation

for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to thee mean