Data analysis

A box plot, also known as a box-and-whiskers plot, is a graphical representation of the Five-Number Summary of a data set. A box is drawn from the lower quartile (Q1) to the upper quartile (Q3); a horizontal line across the box indicates the median. Two whiskers are drawn, one from the lower quartile to the minimum and one from the upper quartile to the maximum. Box plots can be used to make graphical comparisons between data sets and to measure the variation within parts of a data set.

box plot

An interval is a range of values for data. Some common intervals include the interval from the lowest data value to the highest data value and the interval that contains the middle 50% of data.

interval

The median of a data set is the value in the center of an ordered list of the data. It is also the value for which there are as many values above it as there are below it. For example, in the data set {1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 26}, the sixth value has five above it and five below it. This value, 3, is the median. If a data set contains an even number of values, the median is found by taking the mean of the two values in the center of the ordered list.

median

The mode is the most frequently occurring value in a data set. For example, in the data set {1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 26}, the mode is 4, which has a frequency of three. It is possible for a data set to have more than one mode if two or more values each have the highest frequency. It is also possible for a data set to have no mode if all of its values have the same frequency.

mode

The Five-Number Summary of a data set is a five-item list comprising the minimum value, first quartile, median, third quartile, and maximum value of the set. It divides a data set into four sets, each of which contains 25% of the set.

the five-number summary