Another useful way to present data is the relative frequency. Relative frequency is calculated by dividing the frequency of each return interval by the total number of observations. Simply, relative frequency is the percentage of total observations falling within each interval.
h: Describe the properties of data presented as a histogram or a frequency polygon.
A histogram is the graphical equivalent of a frequency distribution. It is a bar chart of continuous data that has been grouped into a frequency distribution. The advantage of a histogram is that we can quickly see where most of the observations lie. To construct a histogram, the class intervals are scaled on the horizontal axis and the absolute frequencies are scaled on the vertical axis.
A second graphical tool used for displaying data is the frequency polygon. To construct a frequency polygon, we plot the midpoint of each interval on the horizontal axis and the absolute frequency for that interval on the vertical axis. Each point is then connected with a straight line.
i: Define, calculate, and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, geometric mean, weighted mean, median, and mode.
A population meanis the entire group of objects that are being studied. To find the population's mean, sum up all the observed values in the population (sum X) and divide this sum by the number of observations (N) in the population.
A sample meanis sum of all the values in a sample of a population divided by the number of values in the sample. The sample mean is used to make inferences about the population mean.