5.1:
Review and Preview
Statisticians use several tools to interpret the data. Measures of central tendencies, such as mean, median, and mode, identify the single value most representative of the data.
To understand how far the values have spread from the mean, one can use the measures of variations, such as range and standard deviation.
Finally, to interpret each value of the data in relation to other data points, one can use the measures of relative standing.
For example, a student receives 85 percent marks on a class test. By comparing this score with the scores of his classmates, one can know whether the student's performance is excellent or poor. This relative comparison can be made by using any of the three commonly used measures of relative standing—percentile,z score, or quartiles.
Percentiles divide data into groups of hundreds and measure where the data lies in those groups. The z score is the standard score used to find the unusual values. A quartile summarizes a group of numbers into four groups visualized using a boxplot.
5.1:
Review and Preview
In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
Percentiles are a type of fractile that partition data into groups with roughly the same number of values. Percentile divides data into 100 groups, with about 1% of the values in each group.
z scores are measures of position in that they describe the location of a value in terms of standard deviations relative to the mean. A z score of 2 indicates that a data value is two standard deviations above the mean, and a negative 3 z score indicates that a value is three standard deviations below the mean.
Quartiles are numbers that divide data into quarters. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data.
This text is adapted from Openstax, Introductory Statistics, Section 2.3 Measures of the Location of the Data and 2.7 Measures of the Spread of the Data